Yes, you can upload the CSS files through Cpanel by following the below steps:-
1) Login into your control panel by using this link :
http://yourdomain.com:2082
2) Once you login click on "File Manager" .
3) After you click on the File Manager icon another browser window will open that will look similar to this screen and click on Public_html folder.
4) Now you are ready to upload files.
Note:: You will many folders . If you mess around with any wrong folder then you can destroy your e-mail, your frontpage extensions and more. So, be careful in what you are doing.