Not an I.Q. test but possibly both a “written” test and a road test every four years when you renew your license. I got my first driver’s license when I was 16 and didn’t have to take a road test because I took driver’s ed, just had to take the written test. I have lived in four different states and each time I have moved I just had to surrender my license from the other state and the new state gives me a license.
And every time I have had to get a new license in the state I moved to or renew my license in any of those states, in almost 40 years of driving, I have never been required to take any kind of road test or another written test, since the age of 16. Apart from my relatively clean driving record, these DMVs really have no idea whether I know how to drive or not. All they know is that I am pretty good at not running into things and not getting tickets.
But, as mentioned, in almost 40 years of driving I have never been required to take a road test and have taken a written test only once. Maybe more should be required of people who drive cars.