Not all issuers require a checking or savings account. And if they do so, it is usually clearly stated in card description. Check your credit score before you apply for a card. When you know your credit score, see what credit cards fit your score and don’t require a checking account.
All credit cards terms, fees and rates mentioned in this article/post are actual on the posting date. See the current products’ Terms & Conditions on the issuing banks' websites.