In the comics, during the 60's era, he had a motorcycle.. then in the early 70's they introduced the Spider-Mobile as a gag, then handicapped Pete by saying he never got a regular Driver's License..
"With Great Power Comes Great Responsibility" Stan Lee, 1962
Yes, here the episodes where he drived a car season 1 -The Power of Doctor Octopus!
season 2 -Blotto -Thunder rumble
season 3 -The Birth Of Micro Man
bonus, not a car or a motorcycle -Phantom From The Depths Of Time: Spider-man pilots a sort of experimental plane (a spaceship recycled from an episode of Rocket Robin Hood, more strange the spaceship was restaured to its stock look despite being completely destroyed by these mechanical beetles, Spidey menaged to drive for a couple of seconds one of these mechanical beetles as well)
-Sand of crime: drive a bulldozer to found Sandman but Sandman got the last word.
Not really a handicap. He lived in New York City where more than half the residents don't have driver licenses. They don't need them due to public transportation.