Google offers git -> App Engine and git <-> Source Repository, so presumably somewhere it offers Source Repository -> App Engine.
But I can't find where... even after twice reading all the Source Repository and App Engine docs I can find, inc. https://cloud.google.com/source-repositories/docs/ .
I'd guess the procedure could be How to manually deploy direct from Bitbucket to Google App Engine? modified to access the SR files. But I can find teh SR files in the GCS VM. Deleting all the $HOME folders I do find http://i.imgur.com/sHQ98Vw.png have no effect on the files shown at Source http://i.imgur.com/o9vqkQl.png .
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