Google offers git -> App Engine and git <-> Source Repository, so presumably somewhere it offers Source Repository -> App Engine
The best way to do this would be to clone the repository to your machine (or Cloud Shell), then use the App Engine deploy tool (https://cloud.google.com/appengine/docs/php/getting-started/deploying-to-app-engine) to deploy your app.
e.g.
gcloud source repos clone $REPO
cd $REPO
gcloud app deploy app.yaml
Ostensible solution (untested by me) here: https://web.archive.org/web/20161119132814/https://cloudplatform.googleblog.com/2016/10/introducing-Google-Cloud-Shels-new-code-editor.html