The phrase "a car picked" is not correct and lacks context to be usable in written English.
It could potentially be used in a sentence where the subject is being described, but it needs additional information to clarify the action or situation.
Example: "A car picked up the passengers at the airport."
Alternatives: "a car was chosen" or "a car was selected."
A few minutes later, a car picked its way through the tree debris.
The next morning, a car picked me up and we sped along a highway 60 miles to Haiphong to catch a high-speed ferry.
The next morning, a car picked me up at 6 30 took me to Greenwich, Conn., where the senior management regrouped and tried to ascertain whom we had lost.
When the children's plea for a 'proper holiday' – one involving flying, not camping – became deafening, we booked flights for Boston, hired a car, picked a hotel for the first night and set off.
It's centred on a murder that took place in 1976: a young man stole a car, picked up a hitchhiker called Randall Adams and later a policeman was shot and killed by someone in the car.
To get to it, Hicks had to climb out his window, shin down the drainpipe to the garage roof, jump from the roof to the ground, and hightail it to the Catholic church behind his house, where Kevin Booth, a friend who had a car, picked him up and then drove both performers to the club.
"Test-driving a car", "picking berries", "following a man".
At last a car picks me up in front of a supermarket.
"But this is not just a game where you go through menus, pick a car, pick a race and go around and around on a track.
You send a request via your iPhone app; a minute later, a car picks you up and drives you wherever you want, at a fraction of the cost of owning your own vehicle.
Buying a car, picking a new pair of glasses or deciding what to do with your 401k?
