The development comes two days after Romney's second-place finish behind former Arkansas Gov. Mike Huckabee in the Iowa Republican caucuses. Josh Romney, a son of Mitt Romney, told reporters the result in Wyoming shows the campaign is "running all over the country," The New York Times reported.
Tom Sansonetti, a member of the Republican National Committee's rules committee, called Saturday "a very historic day for the Wyoming Republican Party."
"Iowa has the first caucus," he said. "New Hampshire has the first primary. But it's Wyoming that elected the first delegates."
However, Wyoming is forfeiting half its usual complement of 28 delegates to the presidential nomination convention in Minneapolis because the state party broke national party rules by holdings its conventions before Feb. 5, the Times said.
Two more delegates will be chosen at the state party convention in May.