Yes, you do burn calories when you’re behind the wheel! The average person will burn 150 to 250 calories per hour by driving a car, and possibly more if they’re driving a large truck or a bus. For reference, the average person burns 60 to 130 calories per hour by sitting and 415 calories per hour by walking.
In short: if you’re looking to lose weight, driving won’t be enough on its own. If you can, it might help to get a bicycle and use that for transport instead. However, it’s definitely nice to know that you’re burning calories while you’re behind the wheel.