A car on a ferry from Sibenik to Zlarin, Obonjan, Kaprije and Zirje

There is a car ferry that connects Sibenik with Zlarin, Obonjan, Kaprije and Zirje.

It is a ferry route 532 run by Jadrolinija and you can get to all of these islands by car, motorbike, scooter, or bicycle all year round.

You can even get a bus on Sibenik to Zirje ferry route, but not to the other of these islands.

So, the answer is yes, you can get a car to all of these islands but on some of them, as they are a car-free zone, you can’t drive around.

The island that you can visit by car and drive around is Zirje:

https://www.croatiaferries.com/sibenik-zirje-ferry.htm

However, the road infrastructure is underdeveloped, all roads on the island are tarmac roads and lanes, so, unless you have a sturdy four-wheel drive 4WD it doesn’t make sense to take a car there. Locals offer taxi/driving services.
Unless you like to walk around, the best option is to take a bicycle there and explore, or once you arrive there, rent a small boat with a local skipper to take you to some nice spots.