Is there any way to use a git repository with the built in SCM functions of Xcode?
You can use Xcode with Git repos. Visual Studio Team Services offers free, private, and unlimited Git repos in the cloud. Not only can you use Xcode, but also Eclipse, Visual Studio, Team Services' own web browser interface, or any other editor/IDE you like. Share code with the first 5 users for free too.
YouTube video: https://youtu.be/S83kn0i4WYs