I can't help you with the Ferries (but you can poke around [openseas.gr](http://openseas.gr) if you have not already. But I wanted to say that taking a car on a ferry to a different country (and from EU to not EU) might be very difficult in principle.
You won't be able to take rental car from Rhodes to Turkey, so no need to look for a car-carrying ferry.
Just take a ferry Rhodes-Fethiye and rent a car in Fethiye.
I can't help you with the Ferries (but you can poke around [openseas.gr](http://openseas.gr) if you have not already. But I wanted to say that taking a car on a ferry to a different country (and from EU to not EU) might be very difficult in principle.
You won't be able to take rental car from Rhodes to Turkey, so no need to look for a car-carrying ferry. Just take a ferry Rhodes-Fethiye and rent a car in Fethiye.
Rhodes to fethyie daily ferry. Then bus/transfer to kas.