You'll probably have to actually clone your repo, then push from it locally, but that should be easy.
Update 19/09/2016: The previous link is broken, the current way to connect to some external repo is treated in the section Connecting a Hosted Repository
App Engine supports "Push to Deploy" which can do almost exactly this!
https://developers.google.com/appengine/docs/push-to-deploy
You'll probably have to actually clone your repo, then push from it locally, but that should be easy.
Update 19/09/2016: The previous link is broken, the current way to connect to some external repo is treated in the section Connecting a Hosted Repository