Deputy Agriculture Secretary John R. Norton III, who had been acting secretary since last Saturday, resigned yesterday, apparently under heavy political pressure from Republicans who want a midwesterner in his job.

Norton said he would go home to Phoenix and resume direction of his large farm operations in Arizona and California.

He refused to explain his decision, saying, "It's my last day, but I have to exercise the politician's prerogative and be circumspect about this."

Late last year Norton said he might have to quit because conflict-of-interest rules made his farms ineligible for federal support programs. Recently, however, he indicated that he would stay.

But after President Reagan announced plans to nominate Richard E. Lyng, a Californian, to succeed John R. Block as secretary, GOP farm-state legislators mounted a dump-Norton drive, saying that if he remained deputy secretary the leadership would be top-heavy with westerners.

Several weeks ago Norton said Senate Majority Leader Robert J. Dole had suggested that he step down to make way for a midwesterner. In the past, the Kansas Republican has floated the name of Duane Acker, retiring president of Kansas State University, as a possible successor.

Norton, a millionaire Republican, said his economic situation was not the deciding factor in his resignation, but he refused to elaborate. He described his decision as "kind of a letdown."

After Block left last Friday to head a wholesale grocery distributors' association, Norton automatically became acting secretary. Department and congressional officials assumed he would remain until Lyng was confirmed by the Senate. And when he appeared at a USDA news conference yesterday morning he gave no indication of resigning.

A Senate Agriculture Committee spokesman said that Lyng's nomination papers have not arrived and that confirmation hearings could not take place for at least a week after that.

Until Lyng is cleared by the Senate, the acting secretary will be Frank W. Naylor Jr., a former California farm credit official who has been undersecretary for small community and rural development since 1981.

Norton became deputy secretary last May after Lyng resigned to start a consulting firm here. Norton was backed by western GOP farm interests who wanted more representation at USDA.