Can I build credit with a shopping credit card?

Generally, you are able to build credit using a credit card if it reports to a major bureau. Some of the store cards report to credit bureaus, but it's better to check this before applying for a card. And sometimes the issuers report only to one bureau, which is not enough for you. If you are worried about your credit history, it's better to build it using a general credit card. If you have bad or limited credit, you may start with a secured credit card and once you improve your credit, you may get a general card and then proceed to a credit card with rewards. General cards give as many rewards as store cards and even more and they don't charge such high fees and APRs, so in a way they may be a better solution.