I can think of 3 things that it affects relative to your score. First, every "hard Inquiry" (credit check) can slightly lower your score. So when you apply and they do a credit check it can lower your score by a point or two. However, having more available credit, assuming you don't use it, lowers your Utilization ratio, (how much credit you have vs how much credit you've used) which can raise your score a couple of points. Third, a new credit card with lower the average age of your credit account. An older average age is better as far as your credit score goes but, again, unless you are applying for new cards weekly you are talking about a point or two. So take the deal! We just took advantage of a Chase offer that gave us $400 cash back just to open the account. Didn't really need (or I should say REALLY DIDN'T need) another credit card but I'm not going to turn down a free $400.