The Intel XDK does not prescribe a source code control system, you can use whichever you prefer or whichever works best for your project.
That said, the Brackets editor that is built into the XDK (on the Develop tab) does include a git extension that is very convenient for use with github accounts, local git repos and private git remote repos. Once you get your git repo(s) setup in your project it works very nicely (I use it all the time for syncing with my git repos, it's easier than using the command-line). When you have the editor open, check the "File --> Extension Manager..." menu item and you'll find the brackets-git extension (docs here https://github.com/zaggino/brackets-git).
I've always setup my git repos by hand when using this extension, so I don't know how well it works at initializing a repo. In any event, once you've got your project setup as a git repo, it works quite nicely.
One thing to be aware of, there are a few files that are hidden from the Brackets file manager view but are part of your project directory (in particular, .xdk files, might be a few others). The git extension will pick those up, but it won't display them in its list of files to commit. I've found that if you want to include them in your git repo (you might want to include the *.xdk file, but not the *.xdke file) you just need to check the "select all" button using the git extension file list checker and then uncheck the files you don't want to use. When you push the commit button you'll see those hidden files in the list of files to be included in the commit. That point can be a little confusing, but will make more sense once you play around with the extension.
Also, the git command-line utilities are NOT installed as part of the extension, they assume that git is already installed on your system and available in the path. See the git extension docs for info on how to install git on your system if you don't already have it there.
