There are many threads on the topic...many recommendations, like Rome in Limo, Rome Cabs, etc. All those threads saying Rome to the port, or the port to Rome, or the port to FCO all have vender recommendations. Plus, if you can manage your bags, there is the option of the train.
However, it is definitely not recommended to arrive the day of sailing. Rome is one of the most amazing cities in the world. Ease your jetlag and see one of the best cities in the world.