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If you didn’t give that person permission to open a credit card in your name, then it is identity theft. You should contact the creditor who issued the card and inform them about the situation. You will also need to contact the credit reporting bureaus as well and put a freeze on your reports. Also, you are supposed to file a report with the police. Because the credit issuer will want to see that kind of official documentation. At the very least you should close the account. Other actions you could take depend on how much was charged and if your relative is willing to pay those charges.