AN AMERICAN GOVERNOR has not been recalled from office since that unhappy fate befell Lynn Frazier of North Dakota in 1921, but it seems about to happen again. In Phoenix this week organizers filed some 388,000 petitions asking for Evan Mecham's recall. An election will be held next spring, after he has been in office just a little more than a year. His plight is all the more surprising in that it comes in one of the nation's most prosperous and vibrantly growing states, and because Mr. Mecham is a conservative Republican in a state known since Barry Goldwater's victories in the 1950s as strongly conservative and Republican.

Mr. Mecham wasted no time in bringing this on himself. Last January when he took office he promptly rescinded the Martin Luther King Jr. holiday established by his predecessor Bruce Babbitt. He endorsed a book by his political mentor that called black children "pickaninnies," and he declared a reporter (the brother of a Republican congressman) a "nonperson" and refused to answer his questions. He said he didn't know what he'd say to Pope John Paul II when he visited the state because he didn't know if he spoke English. Arizona lost millions of dollars of convention business when organizations canceled meetings there to protest the governor's action on the King holiday. A recall movement was started by an avowed homosexual and was shunned for a while by the state's Democrats and newspapers. But as Mecham jokes filled the air waves, and as Mr. Mecham's top aide was indicted on an extortion charge and the state attorney general was investigating a charge that Mr. Mecham's campaign failed to disclose a $350,000 loan (the investigation has since been suspended), signatures proved easy to get.

Gov. Mecham blamed "militant liberals and the homosexual lobby" for the recall movement, but it has received support from most active Democrats, including Mr. Babbitt and Rep. Morris Udall, and from some Republicans as well. Former senator Barry Goldwater said he hoped Mr. Mecham would resign and let State Secretary Rose Mofford, a Democrat, become governor. The Arizona Republic and the Phoenix Gazette called for his resignation. Some will cite Mr. Mecham as proof of the retrograde tendency of American voters, but he is in fact a political accident: an upset winner, after several unsuccessful races, in the 1986 Republican primary and the winner with only 40 percent of the vote in a three-way general election against Democratic nominee Carolyn Warner and Democrat Bill Shulz running as an Independent. It sounds as though the voters of Arizona are about to do the right thing