Clean it off some how and rewrite it, with pen and let it dry longer this time, make sure it won't smear before putting it in your purse or wallet or wherever you keep it :)
Don't worry about it. I never sign my credit cards. I know it's stupid, I just never get around to doing it, and so far it hasn't caused a single problem for me. I'm not telling you not to sign your credit cards, I'm just saying to worry about it.