Yes, but it takes lots of planning before hand and is expensive. It’s about $80-100 each way to take your car. It also limits that you have to go out of Wood’s Hole. We rented a car from Hertz in Vineyard Haven. There are also smaller rental car companies in Oaks Bluff right as you get off the ferry.
You don’t necessarily need a car if you want to stick mostly to Oaks Bluff and Edgartown. If you want to explore the whole island and see all the different beaches, you either need to rent a car or try to arrange a tour. You can arrange a tour when you are purchasing the ferry tickets. If you are planning on renting a car, I would recommend booking it in advance.