Each credit card will have its own qualifying credit score requirement. In many cases, you'll need a credit score of 670 or higher to qualify for a rewards credit card. Applicants with bad credit will most likely have a difficult time getting approved, but people with fair credit (FICO 580 to 669) or poor credit (300 to 579) may qualify for a secured credit card that offers points or cash back on all purchases, including groceries.