Hi,
Using CPanel to upload any file/folder is no such problem.
Do this;
Make a zip file of your folder, for example if i want to upload my eitire web folder which is named as "Test" than make a zip file of this entire folder.
Than go to your CPanel and Click File Manager and go to your destination folder and Upload this zip file on your destination folder.
After uploading, click on this File which should be "Test.zip", and you will see a lot of options in the right side of your Browser window, here you can see an option of Extract File, use it.
(This Extract File option is only comes when you click on any ZIP/RAR File)

This method will also save your Bandwidth, as you are using Compression.

Regards,
masterleous