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.
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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.