When I was new to GIT this scared me, I was afraid I could somehow delete my current project or something like that, but it is rather trivial to add new GIT repo to existing project. All you need to do is add a remote config and do some initializations. Basically you do this
cd existing_folder
git init
git remote add origin git@gitlab.com:my_account/my_repo.git
git add .
git commit -m "Initial commit"
git push -u origin master
In this example we used remote config from gitlab but it could be anything you like.