Ugh. Well, I guess to a degree they HAVE to secure against polluting the little kiddies' minds, but this seems a bit zealous. And suspicious. After all, why your credit card? Why not your driver's license info or your SSN? They're irritatingly patronizing, but I'm suprised at anyone who's not used to it. We're friggin' second-class citizens, everyone seems to treat someone more than 2 years younger than them as subhuman idiots anyhow...
Anyway, if you really want this, enough to compromise someone's credit account, I recommend one of the following:
1. Ask your bloody parents. You're under 18, you're not free from prying eyes, if they really care they'll find and delete it anyhow after all your hard work. They should have few objections normally (after all, you already are in possession of at least two violent games, one VERY so...), except that possibly they don't wanna give out that info.
2. Crack it. It's not like you've never seen a credit card before, imitate the PIN numbers. Make up a name. After an hour's attempt, if you still don't have it (they can't be checking THAT closely, to do it in that time), borrow a card for a few minutes, or find an old one. This is why you always keep an outdated credit card someone forgot to cut up on hand, along with an if necessary fake driver's license.
3. Respond to one of those American Express "You've been pre-approved for this very special deal!" letters. They really don't check. Problem is, if you spend any real amount of actual money on it or end up getting buggered if Activision uses/sells this info, you're dead in every since, including possibly the literal (people take crappy credit records VERY seriously). Advantage is, this is more legal than the others, and most likely to work. It'll just take a few weeks.