The bank account is not an indispensable criterion to be approved for a credit card. Much depends on the type of card you are going to apply for. There are the so-called secured credit cards, which are generally (but not necessarily) issued to people with bad or no credit history. To get such card you must deposit some amount of money to guarantee your ability to pay off your debt. Thus, you can't receive a secured card without an account. If you wish to obtain an unsecured credit card however you can do without a bank account. The much more important thing is to consider your credit report and to learn your credit score. It is the score that defines your creditworthiness. Mind, that if the score is low, unsecured cards for bad credit generally charge higher interest rates and fees. The initial credit limit is rather low; it'll increase gradually as long as you pay all the bills on time. The unsecured cards can be a helpful tool in rebuilding your credit, if you use them properly (make all the payments on time). Look through the page devoted to the cards for bad credit and choose the card you like. Compare all of the terms and conditions attentively. Fill the application and wait for an approval.
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.