This is related to another question I recently asked about storing a non-bare repository in Dropbox for easy movement between computers, so it may be helpful to read that qu
Use gitk as follows
$ gitk path/to/repository/file
In the opened window, under dashed line you can see six digits. The last three are the file permissions.
...
------------------------------- path/to/repository/file -------------------------
index a5e14048..08ce8948 100644
...
In the example above 6 digits are 100644 and file permission is 644