As a newer user to git, I took the following approach. From the command line, I was able to rename a folder by creating a new folder, copying the files to it, adding and commiting locally and pushing. These are my steps:
$mkdir newfolder
$cp oldfolder/* newfolder
$git add newfolder
$git commit -m 'start rename'
$git push #New Folder appears on Github
$git rm -r oldfolder
$git commit -m 'rename complete'
$git push #Old Folder disappears on Github
Probably a better way, but it worked for me.