Yes, you can make an online donation on behalf of a donor. 

You would go into their profile and select Add - Donation Via Page. Once you've selected that a pop up window will appear allowing you to select the donation page you would like to use. When you select the donation page a new tab will appear with that Donation Page. The constituents information should be auto filled. If you have the donors credit card stored in their profile it will allow you to select that card. If not you can just enter the credit card info manually.