"a car full of" is a correct and usable phrase in written English.
You can use it to refer to a car containing something. For example, "We drove away in a car full of groceries."
A car full of protestors crashed into police.
She was the designated driver for a car full of rowdy friends.
A car full of six-footers might also be a tight squeeze.
Laura takes her break outside and passes a car full of loud teen-age boys.
In the fading light, he examined a car full of nervous Pashtuns as it drove past.
"A car full of Jews going down the street singing carols.
The agency arrested two men Monday who were traveling in a car full of explosives.
Driving with a car full of balloons for your child's birthday: minus 11 m.p.h.
Israeli fire hit a car full of journalists in Ramallah on Monday, but caused no casualties.
There was Jordan Davis, whose killer shot into a car full of teenagers over loud music.
Everywhere we went, a motorcycle cop led the way, and a car full of officers followed.
