Are you sure the port is actually damaged? A common issue is lint clogging it up. I had an issue where I had to jiggle the cable to get it to charge and when I finally brought it to an Apple store they disappeared out back and returned with so much lint I don't know how it even fit in the port. You can remove it yourself with a paperclip but I'd take it to the Apple store so that if the port really does get damaged removing the lint they're liable.