You'll want to use a continuous integration system, and there are many to choose from. Probably your top choices for iOS are:
- Jenkins - free, a little complex to use
- Travis-CI - free for open source projects, otherwise paid.
- Xcode Bots - free, comes with Mac OS X Server (free for developers), built by Apple
You'll likely want to install one of these pieces of software on a dedicated server (although Travis is hosted for you, as far as I'm aware). They can all monitor your Git repository and perform a new build whenever you push a commit.