How long should you wait to pay off your auto loan to positvely affect your credit score?

The sooner you pay it off, the better.

Credit agencies rate you based on the amount of debt you can handle, among other things. This mainly pertains to revolving credit, i.e. credit cards, however.

The sooner you can get debt into your name and then rid of it may extend the amount of credit a creditor will lend you in the future. This is just a possibility, as all three 3 major credit bureaus are different.