fraud- what if i pay the debt, can i negotiate to get the card back to use?

I have bad credit from medical bills. I always wanted a "credit card" come to find out someone opened a target card in my name- and charged a couple hundred dollars and now they are after me to pay them. I am wondering and I know this is wierd, but now I am more screwed….Can i try to negotiate with Target to get the card back? I want the target card, i’ll pay the bill. I think paying the 0 is worth it to have the card to actually use. i dont know how long it has been in collections, but when i moved here to my new place about 6 months ago i started to recieve phone calls and letters. Or is it better to just report it as fraud? what will that do to my credit? They said it wasnt an application that someone filled out. It was an offer on a reciept that i threw out offering the card with just a signature or something-which is odd. thanks in advance!

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