I don't understand why you just wouldn't set it up to point to your repo. Then you just click the deploy button and it does the "git pull" etc for you so you don't have to ssh into the server and do it manually, or you can set it up for automatic deployments so whenever you merge into your master branch (or whatever branch you tell it) in git, it will detect it and automatically deploy it to the server.
Since you're already using git, why do you want to skip setting it up?