diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 2a529c2d7b804..3a686c83a6244 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -26,6 +26,7 @@ Changelog
   and :class:`~cryptography.hazmat.primitives.ciphers.algorithms.ARC4` into
   :doc:`/hazmat/decrepit/index` and deprecated them in the ``cipher`` module.
   They will be removed from the ``cipher`` module in 48.0.0.
+* Added support for deterministic ECDSA (:rfc:`6979`)
 
 .. _v42-0-3:
 
diff --git a/docs/hazmat/primitives/asymmetric/ec.rst b/docs/hazmat/primitives/asymmetric/ec.rst
index 75165b6a45364..b5b054e59d895 100644
--- a/docs/hazmat/primitives/asymmetric/ec.rst
+++ b/docs/hazmat/primitives/asymmetric/ec.rst
@@ -47,6 +47,16 @@ Elliptic Curve Signature Algorithms
     :param algorithm: An instance of
         :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`.
 
+    :param bool deterministic_signing: A boolean flag defaulting to ``False``
+        that specifies whether the signing procedure should be deterministic
+        or not, as defined in :rfc:`6979`.
+
+        .. versionadded:: 43.0.0
+
+    :raises cryptography.exceptions.UnsupportedAlgorithm: If
+        ``deterministic_signing`` is set to ``True`` and the version of
+        OpenSSL does not support ECDSA with deterministic signing.
+
     .. doctest::
 
         >>> from cryptography.hazmat.primitives import hashes
diff --git a/src/cryptography/hazmat/backends/openssl/backend.py b/src/cryptography/hazmat/backends/openssl/backend.py
index 406b1ea990a26..eaaaf783f1c5c 100644
--- a/src/cryptography/hazmat/backends/openssl/backend.py
+++ b/src/cryptography/hazmat/backends/openssl/backend.py
@@ -358,6 +358,12 @@ def ed448_supported(self) -> bool:
             and not rust_openssl.CRYPTOGRAPHY_IS_BORINGSSL
         )
 
+    def ecdsa_deterministic_supported(self) -> bool:
+        return (
+            rust_openssl.CRYPTOGRAPHY_OPENSSL_320_OR_GREATER
+            and not self._fips_enabled
+        )
+
     def _zero_data(self, data, length: int) -> None:
         # We clear things this way because at the moment we're not
         # sure of a better way that can guarantee it overwrites the
diff --git a/src/cryptography/hazmat/primitives/asymmetric/ec.py b/src/cryptography/hazmat/primitives/asymmetric/ec.py
index b612b40149d4d..da1fbea13a6e1 100644
--- a/src/cryptography/hazmat/primitives/asymmetric/ec.py
+++ b/src/cryptography/hazmat/primitives/asymmetric/ec.py
@@ -8,6 +8,7 @@
 import typing
 
 from cryptography import utils
+from cryptography.exceptions import UnsupportedAlgorithm, _Reasons
 from cryptography.hazmat._oid import ObjectIdentifier
 from cryptography.hazmat.bindings._rust import openssl as rust_openssl
 from cryptography.hazmat.primitives import _serialization, hashes
@@ -319,8 +320,21 @@ class ECDSA(EllipticCurveSignatureAlgorithm):
     def __init__(
         self,
         algorithm: asym_utils.Prehashed | hashes.HashAlgorithm,
+        deterministic_signing: bool = False,
     ):
+        from cryptography.hazmat.backends.openssl.backend import backend
+
+        if (
+            deterministic_signing
+            and not backend.ecdsa_deterministic_supported()
+        ):
+            raise UnsupportedAlgorithm(
+                "ECDSA with deterministic signature (RFC 6979) is not "
+                "supported by this version of OpenSSL.",
+                _Reasons.UNSUPPORTED_PUBLIC_KEY_ALGORITHM,
+            )
         self._algorithm = algorithm
+        self._deterministic_signing = deterministic_signing
 
     @property
     def algorithm(
@@ -328,6 +342,12 @@ def algorithm(
     ) -> asym_utils.Prehashed | hashes.HashAlgorithm:
         return self._algorithm
 
+    @property
+    def deterministic_signing(
+        self,
+    ) -> bool:
+        return self._deterministic_signing
+
 
 generate_private_key = rust_openssl.ec.generate_private_key
 
diff --git a/src/rust/cryptography-openssl/build.rs b/src/rust/cryptography-openssl/build.rs
index 5e626f7de6141..87e1fa528b22f 100644
--- a/src/rust/cryptography-openssl/build.rs
+++ b/src/rust/cryptography-openssl/build.rs
@@ -12,6 +12,9 @@ fn main() {
         if version >= 0x3_00_00_00_0 {
             println!("cargo:rustc-cfg=CRYPTOGRAPHY_OPENSSL_300_OR_GREATER");
         }
+        if version >= 0x3_02_00_00_0 {
+            println!("cargo:rustc-cfg=CRYPTOGRAPHY_OPENSSL_320_OR_GREATER");
+        }
     }
 
     if env::var("DEP_OPENSSL_LIBRESSL_VERSION_NUMBER").is_ok() {
diff --git a/src/rust/src/backend/ec.rs b/src/rust/src/backend/ec.rs
index 624b753c07cba..5e1e657082719 100644
--- a/src/rust/src/backend/ec.rs
+++ b/src/rust/src/backend/ec.rs
@@ -274,7 +274,7 @@ impl ECPrivateKey {
             ));
         }
 
-        let (data, _) = utils::calculate_digest_and_algorithm(
+        let (data, _algo) = utils::calculate_digest_and_algorithm(
             py,
             data.as_bytes(),
             signature_algorithm.getattr(pyo3::intern!(py, "algorithm"))?,
@@ -282,6 +282,27 @@ impl ECPrivateKey {
 
         let mut signer = openssl::pkey_ctx::PkeyCtx::new(&self.pkey)?;
         signer.sign_init()?;
+        let deterministic: bool = signature_algorithm
+            .getattr(pyo3::intern!(py, "deterministic_signing"))?
+            .extract()?;
+        cfg_if::cfg_if! {
+            if #[cfg(CRYPTOGRAPHY_OPENSSL_320_OR_GREATER)]{
+                match deterministic {
+                    true => {
+                        let hash_function_name = _algo.getattr(pyo3::intern!(py, "name"))?.extract::<&str>()?;
+                        let hash_function = openssl::md::Md::fetch(None, hash_function_name, None)?;
+                        // Setting a deterministic nonce type requires to explicitly set the hash function.
+                        // See https://github.com/openssl/openssl/issues/23205
+                        signer.set_signature_md(&hash_function)?;
+                        signer.set_nonce_type(openssl::pkey_ctx::NonceType::DETERMINISTIC_K)?;
+                        },
+                    false => signer.set_nonce_type(openssl::pkey_ctx::NonceType::RANDOM_K)?,
+                };
+            } else {
+                assert!(!deterministic);
+            }
+        }
+
         // TODO: This does an extra allocation and copy. This can't easily use
         // `PyBytes::new_with` because the exact length of the signature isn't
         // easily known a priori (if `r` or `s` has a leading 0, the signature
diff --git a/tests/hazmat/primitives/test_ec.py b/tests/hazmat/primitives/test_ec.py
index a558af3b9b709..9981353ce8427 100644
--- a/tests/hazmat/primitives/test_ec.py
+++ b/tests/hazmat/primitives/test_ec.py
@@ -16,6 +16,10 @@
 from cryptography.hazmat.bindings._rust import openssl as rust_openssl
 from cryptography.hazmat.primitives import hashes, serialization
 from cryptography.hazmat.primitives.asymmetric import ec
+from cryptography.hazmat.primitives.asymmetric.ec import (
+    EllipticCurvePrivateKey,
+    EllipticCurvePublicKey,
+)
 from cryptography.hazmat.primitives.asymmetric.utils import (
     Prehashed,
     encode_dss_signature,
@@ -27,6 +31,7 @@
     load_fips_ecdsa_signing_vectors,
     load_kasvs_ecdh_vectors,
     load_nist_vectors,
+    load_rfc6979_vectors,
     load_vectors_from_file,
     raises_unsupported_algorithm,
 )
@@ -508,6 +513,70 @@ def test_signature_failures(self, backend, subtests):
                         signature, vector["message"], ec.ECDSA(hash_type())
                     )
 
+    def test_unsupported_deterministic_nonce(self, backend, subtests):
+        if backend.ecdsa_deterministic_supported():
+            pytest.skip(
+                f"ECDSA deterministic signing is supported by this"
+                f" backend {backend}"
+            )
+        with pytest.raises(exceptions.UnsupportedAlgorithm):
+            ec.ECDSA(hashes.SHA256(), deterministic_signing=True)
+
+    def test_deterministic_nonce(self, backend, subtests):
+        if not backend.ecdsa_deterministic_supported():
+            pytest.skip(
+                f"ECDSA deterministic signing is not supported by this"
+                f" backend {backend}"
+            )
+
+        supported_hash_algorithms: typing.Dict[
+            str, typing.Type[hashes.HashAlgorithm]
+        ] = {
+            "SHA1": hashes.SHA1,
+            "SHA224": hashes.SHA224,
+            "SHA256": hashes.SHA256,
+            "SHA384": hashes.SHA384,
+            "SHA512": hashes.SHA512,
+        }
+        vectors = load_vectors_from_file(
+            os.path.join(
+                "asymmetric", "ECDSA", "RFC6979", "evppkey_ecdsa_rfc6979.txt"
+            ),
+            load_rfc6979_vectors,
+        )
+
+        for vector in vectors:
+            input = bytes(vector["input"], "utf-8")
+            output = bytes.fromhex(vector["output"])
+            key = bytes("\n".join(vector["key"]), "utf-8")
+            if "digest_sign" in vector:
+                algorithm = vector["digest_sign"]
+                assert algorithm in supported_hash_algorithms
+                hash_algorithm = supported_hash_algorithms[algorithm]
+                algorithm = ec.ECDSA(
+                    hash_algorithm(),
+                    deterministic_signing=vector["deterministic_nonce"],
+                )
+                private_key = serialization.load_pem_private_key(
+                    key, password=None
+                )
+                assert isinstance(private_key, EllipticCurvePrivateKey)
+                signature = private_key.sign(input, algorithm)
+                assert signature == output
+            else:
+                assert "digest_verify" in vector
+                algorithm = vector["digest_verify"]
+                assert algorithm in supported_hash_algorithms
+                hash_algorithm = supported_hash_algorithms[algorithm]
+                algorithm = ec.ECDSA(hash_algorithm())
+                public_key = serialization.load_pem_public_key(key)
+                assert isinstance(public_key, EllipticCurvePublicKey)
+                if vector["verify_error"]:
+                    with pytest.raises(exceptions.InvalidSignature):
+                        public_key.verify(output, input, algorithm)
+                else:
+                    public_key.verify(output, input, algorithm)
+
     def test_sign(self, backend):
         _skip_curve_unsupported(backend, ec.SECP256R1())
         message = b"one little message"
diff --git a/tests/utils.py b/tests/utils.py
index 595e8dc04e1cc..f8bbcbdb8b000 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -701,6 +701,57 @@ def load_kasvs_ecdh_vectors(vector_data):
     return vectors
 
 
+def load_rfc6979_vectors(vector_data):
+    """
+    Loads data out of the ECDSA and DSA RFC6979 vector files.
+    """
+    vectors = []
+    keys: typing.Dict[str, typing.List[str]] = dict()
+    reading_key = False
+    current_key_name = None
+
+    data: typing.Dict[str, object] = dict()
+    for line in vector_data:
+        line = line.strip()
+
+        if reading_key and current_key_name:
+            keys[current_key_name].append(line)
+            if line.startswith("-----END"):
+                reading_key = False
+                current_key_name = None
+
+        if line.startswith("PrivateKey=") or line.startswith("PublicKey="):
+            reading_key = True
+            current_key_name = line.split("=")[1].strip()
+            keys[current_key_name] = []
+        elif line.startswith("DigestSign = "):
+            data["digest_sign"] = line.split("=")[1].strip()
+            data["deterministic_nonce"] = False
+        elif line.startswith("DigestVerify = "):
+            data["digest_verify"] = line.split("=")[1].strip()
+            data["verify_error"] = False
+        elif line.startswith("Key = "):
+            key_name = line.split("=")[1].strip()
+            assert key_name in keys
+            data["key"] = keys[key_name]
+        elif line.startswith("NonceType = "):
+            nonce_type = line.split("=")[1].strip()
+            data["deterministic_nonce"] = nonce_type == "deterministic"
+        elif line.startswith("Input = "):
+            data["input"] = line.split("=")[1].strip(' "')
+        elif line.startswith("Output = "):
+            data["output"] = line.split("=")[1].strip()
+        elif line.startswith("Result = "):
+            data["verify_error"] = line.split("=")[1].strip() == "VERIFY_ERROR"
+
+        elif not line:
+            if data:
+                vectors.append(data)
+                data = dict()
+
+    return vectors
+
+
 def load_x963_vectors(vector_data):
     """
     Loads data out of the X9.63 vector data