Yes, there is. Take the metro (subway). You can get a combination train/subway ticket in Civ and you would pay a LOT less than a taxi is going to cost you. The metro station is right there at the Termini station where you will be arriving from Civ. There is a Metro station about 1/4 to 1/2 mile from the Vatican. Taking a Taxi from the termini station is an option but with traffic, I'm not sure its a time saver.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007