Can a 16 year old buy a car if they pay for it in full in cash?

Yes but with contingencies. Some states require you to have auto insurance before leaving lot, a 16 your old (as a minor) can't get insurance without an adult also signing the policy. While there is no law against selling a car to a minor, a lot of dealers out there won't allow a minor to sign the sales agreement without an adult (parent or guardian) also signing. That's because a minor can't enter into a legally binding contract, and that makes a dealership nervous. Large sums of cash also make dealers nervous too, lol. If the purchase is over 10K in cash, you'll be asked to sign a CTR or cash transaction report which will be filed with the IRS. The dealer may also file a SAR, suspicious activity report, if they suspect anything hinky, and that report is done without informing you. TBH, buying a car for a large amount of cash is dumb. They are terrible investments. Put the money in a bank, make a down payment and work with dealer to get favorable terms (or use your own bank as a car loan originator). You'll help your credit rating, and if the car is wrecked in a few months, the insurance deals with the payoff, and you won't have squandered all the cash.

As a minor your may have a problem having your name as owner of the car but you can assign that to someone you trust...be careful. Best to call a notary and see. But cash should make you the buyer of the car. And cash means you won't have to deal with a bank who can not enter an loan agreement with you without a cosigner who is a legally responsible adult. Also find out what car insurance will cost you.

If your parents are involved I would say no problem at all. You may have a problem as a minor if you try to do the deal on your own.