There is a car park which holds 600 cars and costs £7 per day but the best advise is to contact 01255 242000 for further details on car parking at the port. Hope this helps.
There is a large car park adjacent to the cruise terminal. When I was there 2 years ago, you could not book in advance, you just turned up and paid on arrival. Unlike Southampton, you self park but there are loads of porters who collect your luggage from your car, then you walk into the terminal with your hand luggage. It was a little cheaper than Southampton.