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Almost all credit issuers will request your credit report if you apply for their credit card. A single inquiry won't affect your credit score significantly, if at all. Your credit score will be affected only if you are applying for several credit cards in a row.
Check your credit scores Check your credit scores to make sure your credit is fair. And if it is, you can consider applying for the Credit One Bank® Platinum Visa® for Rebuilding Credit. This is an unsecured Visa credit card with rather low annual fee. The activity on this card will be reported to the major credit bureaus so you will be able to improve your credit history.
If you are not sure whether you will be approved or not, you can look at secured credit cards. These cards require a collateral deposit of about $200, so you have more chances of getting approved.