diff --git a/cloudbuild/scorecard-tag.yaml b/cloudbuild/scorecard-tag.yaml
index 92181eeb046..863d00ef122 100644
--- a/cloudbuild/scorecard-tag.yaml
+++ b/cloudbuild/scorecard-tag.yaml
@@ -13,12 +13,28 @@
 # limitations under the License.
 
 steps:
-- id: 'Get Git history'
-  name: 'gcr.io/cloud-builders/git'
-  args: ['fetch', '--unshallow', '--tags', 'origin', '$COMMIT_SHA']
-- name: 'gcr.io/cloud-builders/docker'
-  args: ['build', '.',
-    '-t', 'gcr.io/openssf/scorecard:stable',
-    '-t', 'gcr.io/openssf/scorecard:$TAG_NAME',
-    '-f', 'Dockerfile']
+  - id: Get Git history
+    name: gcr.io/cloud-builders/git
+    args:
+      - fetch
+      - '--unshallow'
+      - '--tags'
+      - origin
+      - $COMMIT_SHA
+  - id: Get tag commit
+    name: gcr.io/cloud-builders/git
+    entrypoint: bash
+    args:
+      - '-c'
+      - >-
+        git rev-list -n 1 tags/$TAG_NAME > /workspace/commit-sha.txt
+  - id: Push docker tag
+    name: gcr.io/cloud-builders/docker
+    entrypoint: bash
+    args:
+      - '-c'
+      - >-
+        docker pull gcr.io/openssf/scorecard:$(cat /workspace/commit-sha.txt) &&
+        docker tag gcr.io/openssf/scorecard:$(cat /workspace/commit-sha.txt) gcr.io/openssf/scorecard:$TAG_NAME &&
+        docker push gcr.io/openssf/scorecard:$TAG_NAME
 images: ['gcr.io/openssf/scorecard']