Contact your lender and request novation of the loan. Through novation the bank agrees to modify the terms of your original contract. Request that the car loan be transferred into your name only. Your lender will request that you submit copies of various financial documents proving that you can afford the monthly payments on your own. You will also need to submit a copy of the divorce decree granting you full ownership of the vehicle. The exact documentation necessary for novation of the loan will vary depending on the lender.
Refinance the vehicle. By refinancing the car, you are taking out a new loan to pay off the current loan. Provided you take out the new loan on your own, your ex-spouse's name will no longer appear within the loan paperwork, and you will take over full responsibility for making payments. Refinancing is only possible if the value of the car exceeds the amount you still owe on the current loan.
Take out a personal loan to pay off the car if you owe more on the vehicle than it is currently worth. Unlike a refinance loan, a personal loan isn't tied directly to the vehicle. Thus, the vehicle's value isn't a factor in determining whether or not you qualify. Personal loans typically carry stricter credit and income requirements than refinance loans.