Visual Studio, GIT, and SQL Scripts
Sure you can, that's what I do with my projects. Have a look:

Create a new Project, I use SQL Server Database Project because I generally end up adding more than just scripts.



Add items. Scripts in this case.



Go the Team Explorer and select GitHub (or TFS if that's what you're going to work with)



I'm going to create a new Private Repository.



Done!



Now Push the changes...



Finish!