Liberty, a three-year-old hen, set off four weeks ago with 3,000 other birds from Nantes, France, for what should have been a nine-hour race home to Derbyshire.
But instead of flapping back to the rainy Peak District she landed on the cruise liner and took a detour to America and back.
She was found on the sun deck of the QE2, which left Southampton on 25 June bound for Independence Day celebrations in New York.
Crew members captured the feathered freeloader and contacted the Royal Pigeon Racing Association after spotting the identification tag on her leg.
Owner Vince Webster, 47, from Youlgreave, Derbyshire, said the pigeon had earned her name after the ocean-going escapade.
"She didn't have a name before, but she must have seen the Statue of Liberty and it's an appropriate name," he said.
Liberty was one of five pigeons found on board as the QE2 approached the Caribbean, said Mr Webster.
"They caught two, mine and one from Sheffield which I think was in the same race, but the other three flew off.
"There are always a few that go astray and get back eventually, but America is a long way to divert.
"She probably picked up the QE2 in the Channel, or off the French coast in the Atlantic - it was foggy.
"She probably thought it would be nicer to have a holiday than come home and go in another race."
A Cunard spokesman said the pigeons probably got on board at Southampton.
"They were found on the sun deck - they were having quite nice weather in the Atlantic at the time," he said.
Crew members decided to catch the pigeons and keep them in kennels usually used for passengers' pets.
Mr Webster, who has raced pigeons for 34 years and keeps 90, said there would be no more slacking for Liberty.
"Hopefully she has learnt from its mistakes," he said.
"She went missing once before and came back with a broken leg and smashed breast bone after probably flying into a wire. But I hadn't written it off this time."