I would love for someone to post the terms of this card. This should include any upfront fees, any annual fees, any service fees, credit limit range and interest rate. I looked around on the net and could not find them anywhere which makes my suspicious of the deal you might get.
I do not understand the logic of a credit card helping someone pay off debt. How can using a credit card help pay off debt? You create debt when using credit not pay off debt.
Anyway, I don't know if the card is legit but my guess is the terms are probably not that great. I think it is one of those cards that requires upfront fees of a few hundred dollars to open and then you get a $300 limit or so at a high interest rate.
If you want to improve your credit score then clean up the bad debt and watch the slow pays and late pays. If you feel you need a credit card then apply for one with no application fee, no annual fee and try to keep the interest rate low. I do not have or use credit cards anymore. A debit card works as good and you will not end up in debt.