Rome is served by the port of Civitavecchia, but isn't actually a cruise port. In total, Civitavecchia is the seventh most popular cruise port, departure point of around three hundred and ten sailings per year from Norwegian, Royal Caribbean, MSC and more to the Mediterranean and Europe, along with other places.
Cruises scheduled from Rome during the the peak season of summer are much more expensive than the low months of winter and fall. On average Rome is moderately inexpensive compared to other ports. The illustration below shows the monthly average cost per day for cruises from Rome.