Currently there is a .drush folder in my user profile on my mac. However, is it possible to move it into my git repo? How does one move it? If I drag and drop it, then run a drush command, the folder is remade in my user profile folder.
No. Your Mac is running a version of the Unix operating system.
Files and directories starting with a dot (.) in Unix are hidden system files/directories and should not be moved or deleted unless you know what you're doing.