diff --git a/.github/workflows/docs-check-links.sh b/.github/workflows/docs-check-links.sh
new file mode 100755
index 0000000000..888c114826
--- /dev/null
+++ b/.github/workflows/docs-check-links.sh
@@ -0,0 +1,18 @@
+#!/usr/bin/env bash
+set -e
+
+# Check that documentation links work
+
+# The next line returns code 200 only if the page exists
+link_code="$(curl -s -o /dev/null -w "%{http_code}" $URL)"
+
+# Find bad links
+set +e
+good_links="200"
+if [[ "${link_code}" != good_links ]]; then
+    echo "One or more links in the documentation failed:" >&2
+    echo $link_code  >&2
+    exit 1
+fi
+
+exit 0
diff --git a/.github/workflows/docs-check-links.yml b/.github/workflows/docs-check-links.yml
new file mode 100644
index 0000000000..c6bf847280
--- /dev/null
+++ b/.github/workflows/docs-check-links.yml
@@ -0,0 +1,28 @@
+name: Check documentation links
+
+on:
+  push:
+    # Run when a change to these files is pushed to any branch. Without the "branches:" line, for some reason this will be run whenever a tag is pushed, even if the listed files aren't changed.
+    branches: ['*']
+    paths:
+      - 'doc/**'
+
+  pull_request:
+    # Run on pull requests that change the listed files
+    paths:
+      - 'doc/**'
+
+  # Allows user to run this workflow manually from the Actions tab
+  workflow_dispatch:
+
+jobs:
+  link-checker:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Check documentation links
+        run: |
+          .github/workflows/docs-check-links.sh
+        env:
+          # Use GITHUB_TOKEN to avoid rate limiting when checking GitHub links
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+