The refugees were floating on a row boat that appeared to be attached to barrels, with backpacks and paddles inside.
The aptly-titled Independence of the Seas cruise ship chaperoned the men by sailing alongside and watching to make sure they were safe until the US Coast Guard arrived and picked them up.
Passenger Mark Sims said that at first others believed the refugees were pirates trying to get on the ship.
There were more than 4,000 passengers and 1,500 crew members on board at the time.
This isn’t the first time a Royal Caribbean ship picked up Cuban refugees.
Just last month Freedom the Seas picked up seven Cubans who had been out in the ocean with only crackers and water for ten days.
The US Coast Guard picked up the passengers and provided aid, according to Yahoo!.