Even if you can find a work around to add the .git directory to your repo, you should not do this. Instead, you should add the files directly to your repo. If you want, you can maintain the change history with a little bit of git-foo. From the folder of the repo where you want to add the external git project, do the following
git checkout master
git remote add external <directory or URL for the external repo>
git pull external master
This will merge the master branch from the external repo into your current repo. You can also checkout any branch from the external repo with something like
git checkout -b external/master external/master
Now you can make changes or merge from the current project. You can continue to use any git commands you wish from here.
.gitdirectory to your repo is the correct solution. You should add the files you want directly to your repo instead.