It depends on the credit card you choose. Usually there is no checking account requirement for student credit cards. For example, consider the Discover it® Student Cash Back credit card. It does not require you to have a checking account and there is no annual fee. And you will be able to earn cash back on purchases.
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All rates and fees, and other terms and conditions of the products mentioned in this article/post are actual as of the last update date but are subject to change. See the current products' Terms & Conditions on the issuing banks' websites.