In modern-day usage the only accepted spelling is earned in all forms of English, even if you say it as "earnt". For Americans, accustomed to learned, smelled and dreamed as their only options, this little conumdrum is never a problem.
There is conflicting advice on the origin of 'earnt'. Some internet sources state that it is an archaic (out of date/use) form of earned. They will point out that Charles Dickens used it in 1884, yet unlike learnt, dreamt and smelt, 'earnt' does not feature in the OED as a variant. A google search (March 2009) reveals 14,100,000 instances of earnt, but the British National Corpus (1980--1993), which has 100 million words, contains only eight instances of earnt.
About the author
Jesse Karjalainen is the author of The Joy of English: 100 conversations about the English Language, Cannibal – the language and history of the discovery of the New World, and Roanoke – the language and history of Early Colonial America.