diff --git a/.github/workflows/packing.yml b/.github/workflows/packing.yml
index 89565795..e3cc8cb8 100644
--- a/.github/workflows/packing.yml
+++ b/.github/workflows/packing.yml
@@ -268,3 +268,63 @@ jobs:
           path: rpm_dist
           retention-days: 1
           if-no-files-found: error
+
+  run_tests_rpm:
+    needs: pack_rpm
+
+    # We want to run on external PRs, but not on our own internal
+    # PRs as they'll be run by the push to the branch.
+    #
+    # The main trick is described here:
+    # https://github.com/Dart-Code/Dart-Code/pull/2375
+    if: (github.event_name == 'push') ||
+      (github.event_name == 'pull_request' &&
+        github.event.pull_request.head.repo.full_name != github.repository)
+    runs-on: ubuntu-20.04
+
+    container:
+      image: ${{ matrix.os }}.${{ matrix.dist }}
+
+    strategy:
+      fail-fast: false
+
+      matrix:
+        os: []
+        dist: []
+        include:
+          - os: fedora
+            dist: 34
+          - os: fedora
+            dist: 35
+          - os: fedora
+            dist: 36
+
+    steps:
+      - name: Clone the connector repo
+        uses: actions/checkout@v3
+
+      - name: Setup Python and test running tools
+        run: dnf install -y python3 python3-libs python3-pip git make
+
+      - name: Remove connector source code
+        run: python3 .github/scripts/remove_source_code.py
+
+      - name: Install tarantool
+        run: |
+          curl -L https://tarantool.io/yeohchA/release/2/installer.sh | bash
+          dnf install -y tarantool tarantool-devel
+
+      - name: Download RPM artifacts
+        uses: actions/download-artifact@v3
+        with:
+          name: rpm_dist
+          path: rpm_dist
+
+      - name: Install the package from rpm artifacts
+        run: dnf install -y rpm_dist/python3-tarantool-*.noarch.rpm
+
+      - name: Install test requirements
+        run: pip3 install -r requirements-test.txt
+
+      - name: Run tests
+        run: make test-pure-install