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There are not so many unsecured credit card offers for poor credit. The optimal variants for such credit are secured credit cards or prepaid cards. However, you can consider First PREMIER unsecured credit cards, but to apply for these cards you need to have a checking account.
So in general, if you don’t have a checking account or any bank account it will be hard to find an unsecured credit card when your credit is poor. And if you want to build or rebuild your credit it is worth applying for an unsecured credit card which reports to major credit bureaus.