Can I use my car loan payments as a deduction?

Interest on a personal loan, other than a home mortgage, is never deductible.

If the car is used for a schedule C self-employment business, there are two ways of deducting your vehicle expenses, one of which would include the interest, proportional to your actual business use of the car. 

If it is a car personal loan, the answer is no. If you are self-employed in your own business, you can deduct it if you use actual expenses in claiming vehicle expenses. if you deduct mileage, however, then you cannot deduct it.