Adding GIT support to existing project in IntelliJ IDEA

You may need to add git to the list of version control in the settings

settings > Version Control

then make sure that git is listed in the table as a VCS

I had to do this otherwise git wasn't listed in the VCS menu in the menu bar.

I have successfully opened a Maven subproject within IDEA. Naturally, it hasn't enabled Git integration automatically. From VCS menu I have selected "Enable Version Control Integration" and chose "Git" from submenu.

Then IDEA complained that there is no .git folder within the project and offered to select parent .git folder. I did it and everything worked as expected.

If you don't have Git option in VCS menu, this might be a bug. Try to disable SVN plugin and see if that helps (I don't have SVN plugin in my IDEA).