What service provider is it?
If it's Turkcell then if you *don't* have any top up cards your options are limited. As far as I remember, to top up by credit card on the web site your credit card has to be pre-registered with Turkcell - need to fill in a form and take the form and your passport to a Turkcell Extra shop, or do it by post to head office.
You *can* top it up through your (Turkish) online banking; most of the Turkish banks have this facility. If you don't have a Turkish bank account, maybe you know someone who does?
Alternatively, get someone in Turkey to buy a top up card and send you the number...
JF