No, you have to be 21. However, if you are nice to people, they will buy you drinks. My kids were cadging drinks when they were 15 and 17 and I had no idea. My kids are rotten, but nice.
The islands themselves tend to be a bit more lenient, the drinking age is 18 on some of them. Just don't get sloppy and miss the boat.
And how old is your friend? Some cruises require that at least one person be 25 (Carnival), other's require that one passenger be 21. If the parents are along, they can be under 21 as long as they are in a cabin adjacent to the parents. That's what we do.