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Right now there does not appear to be Heb Rewards credit card available, but you can join their rewards program, which does not require a credit score. That said when applying for a store or general rewards credit card it's usually a good idea to wait until you get your score up into the 660-719 range so you can be fairly certain that you will get the card you want. There are credit cards available designed specifically or people who are looking to boost their score, repair credit or get a credit history. They usually have no or low rewards associated with them but if you look around you may find one that waives the annual fee, comes with some perks, and/or offers a promotional APR.