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It depends on your preferences. If you want a credit card issued by Discover then you should have good-to-excellent credit history. To get approved for Discover you should show high credit score, regular payment history, and established credit. The exception is student credit cards and secured credit card. If you are a student you may be able to get a Discover credit card for students with fair credit history.

But if you want a credit card serviced by Discover Payment Network and issued by any other bank, you may be able to find a card that fits bad credit history.