Is there any way I can add a credit card to my iTunes account without my computer?

You can’t use a credit card on the iPhone. I’m guessing you have your iTunes account set up already on the iPhone, if you do just buy an iTunes gift card and redeem it on the App Store.

I don’t think you quite understood the question, maybe I was unclear. What I meant was, I wanted to add a credit card without my computer. Yes I have my account setup with my phone, but I want to know if there’s anyway I can do it other than on the computer’s iTunes? I know I can’t add a card through iTunes or the app store on the iPhone. Perhaps online somewhere? Maybe a secured website??

I think you just answered your own question!

I understood your question, and the answer is no.

You need iTunes to change your iTunes account – can’t do it through a website or the iPhone.

I recommend you buy a Gift Card and redeem it through the App Store on your iPhone.

For more information – read here.

You could always borrow a friends computer and run iTunes on there to add your credit card.