I am trying to import an eclipse project with version control system into Android Studio.
Support for direct eclipse project import was added in Android-Studio vers
The import process does not make this easy. But here's something to try:
Let Android Studio do what it wants to do. It creates a file in the root of the new copy of the project which shows what was moved where.
Make a fresh (scratch) copy of the original git repository. Use "git mv" commands to duplicate the directory structure changes which Android Studio made. Commit the changes.
Copy the resulting .git directory into the project made by Android Studio. Use "git status" there to see how the result of the import process differs from what you did in your scratch copy of the project. At this point you might just choose to commit the remaining differences right there.