Did you know your dad was using your credit card at the time? How about a month later when it showed up on your bill, did you notify the credit card company that it was an unauthorized charged? If your answers are yes and no, then it's your debt. How old is this debt?
Regardless of the above, your only recourse at this time is to sue your dad for the money. You may have statute of limitation/statute of frauds issues since you had no written contract for your dad to pay this debt.
Ask your day for the money to repay this. If he refuses, consult a lawyer to see if you still have a claim and decide if you're willing to pursue it.