I would take the train to Constitutional Sq and a taxi from there.
From Civit ..... take the train about three times an hour and 45 mins to an hour 15 depending on type of train. If coming off a cruise ship the train station will be jammed and it may take longer to buy a ticket than the ride to Rome. SOOOO --- at any other port in Italy find a local train station and buy a Regionale train ticket from Civit... to Rome. When you hit the train station just outside the port entrance (quarter mile down the beach), validate (time stamp) the Regionale ticket in a green/blue/yellow box track side (watch locals do it) and jump the first R train to Rome. It will be the slowest train but totally faster than buying a ticket in Civit..