Since SSMS is (more or less) a custom version of Visual Studio, you might be able to use a solution intended for VS:
Using Git with Visual Studio
Alternatively, manage your DB source code in Visual Studio from the beginning, not in SSMS. That way (at least in VS2010) you have database projects, integrated deployment and unit testing etc. Or continue using SSMS and check in your code from an external tool when you're ready (not so convenient, of course).
But it depends on exactly what you're doing: SSMS is a DBA tool, VS is a developer tool. Either way, you should be using some form of source control, but it's not clear from the question exactly what sort of files you need to version.