I'd have to say no.
A TARDISes ability to change shape comes from the chameleon circuit. The Doctor's TARDIS is of course broken in this respect, but when working it disguises itself as something to blend in with its surroundings. And that's all it is - a disguise.
Consider this: in The Empty Child, the Ninth Doctor expresses surprise when the phone on the outside of his TARDIS rings:
How can it be ringing? It's not even a real phone. It's not connected...
If the telephone on the outside of the TARDIS is not a real phone, then were a TARDIS with a working chameleon circuit to transform into a car, it would not be a real, working car.
The Eleventh Doctor did use the exterior phone on the outside of the TARDIS a couple of times, but the first time he is shown using a phone is at the end of The Beast Below when the phone is actually on the TARDIS console. It would seem that the Eleventh Doctor found a way to divert the phone to the dummy outside. No other Doctor has used it as a phone before or since.
Crucially, the inside of the TARDIS apparently remains the same even when the exterior changes. So if it were to appear as a vehicle externally, there would be no car engine to propel it as a car inside.
Could a TARDIS in the shape of a car mimic the movement of a car? Well, the TARDIS can travel through time and space, so it is capable of travelling through physical space in its own right. Examples of this happening include The Runaway Bride, when The Doctor piloted the TARDIS in a car-chase to rescue Donna, and The Day of The Doctor when the War Doctor crashed it through a wall. So the TARDIS can move about if it needs to, we just generally see it materialise on a planet surface, and dematerialise when it needs to return to orbit.
However, I don't believe that the TARDIS could take the shape of a car and then move in such a way that imitates a car. The way that the TARDIS is seen to move through physical space, rotating or spinning as seen in many episodes of both classic and modern Doctor Who, is nothing to do with the current appearance of The Doctor's TARDIS. For example, in Spyfall, the Master's TARDIS is in the shape of a house and is seen flying next to a plane, gently rotating in a similar manner. That is evidently how a TARDIS moves, whether the chameleon circuit is engaged or not and whatever form it has taken. Presumably then, if it was to take the form of a car it would still have to move in the same fashion.
I should add that all of the above is based on the Mark III Type 40 TARDIS possessed by The Doctor. These are apparently outdated and were decomissioned by the Timelords.
On a personal note, I sincerely hope that the series writers don't ever try to turn Doctor Who into the Transformers.