Rome is not actually a cruise port, but is served by the port of Civitavecchia. In total, the port of Civitavecchia is the eighth busiest port in the world, departure point of more than two hundred and eighty cruises yearly from Royal Caribbean, Celebrity, MSC and more to the Mediterranean and Europe.
On average Rome is somewhat expensive compared to other ports. See the diagram below for the average cost per day by month. Cruises leaving from Rome during the the peak season of summer are much more expensive than the the low season of winter.