Alexander M. Haig Jr. was sworn in as secretary of state yesterday and told a cheering crowd of State Department employes that President Reagan had "clearly enaunciated his intention" that Haig play the leading role in formulating, conducting and explaining American foreign policy.

Haig, choosing a theological analogy, said he would be Reagan's "vicar" -- agent of a higher authority -- in conducting the foreign relations of the new administration.

Even as he was giving these assurances upon his arrival at the State Department, Haig was confronting, and apparently overcoming, the first challenge to his authority.

That challenge came from a group of approximately 16 senators, mostly from the far-right spectrum of the Republican Party, who are unhappy about Haig's choices to fill the department's principal sub-Cabinet jobs. This group, led by Sen. Jesse Helms (R-N.C.), has complained to Haig that they regard many of his expected aides as too liberal to carry out the conservative mandate promised by Reagan in the presidential campaign.

During his Senate confirmation hearings, Haig frequently adopted a hard-line, bellicose tone reminiscent of the Cold War. But in choosing his key subordinates, although they are not officially announced, he is known to have picked mainly moderate Republicans a political technocrats and career Foreign Service officers with experience in both Republican and Democratic administrations -- people whose views generally fall within the mainstream of the bipartisan tradition that has characterized foreign policy since World War II.

That has been taken as an encouraging sign of continuity on broad policy principles within the traditional American foreign policy establishment and the career Foreign Service. But it also has evoked intense suspicion amd, in some cases, feelings of betrayal from hard-core ideological conservatives who fervently supported Reagan's candidacy on the grounds that he would enunicate a sweeping mandate for change in the direction of conservative ideas.

Helms, acting on behalf of the ultraconservative camp, last week sent a letter to Haig questioning some of his proposed appointments. That paralled a similar rumble of discontent from the ideological ultras that saw Helms vote against confirmation of Reagan's defense secretary, Caspar Weinberger, and mount a rear-guard action to hold up confirmation of Frank to hold up confirmation of Frank to hold up confirmation of Frank to hold up confirmation of Frank Carlucci as Weinberger's deputy.

At the State Department, the conservative fire is understood to be directed primarily against Lawrence S. Eagleburger, a career officer who is Haig's choice as assistant secretary for European affairs. Eagleburger, who was Henry Kissinger's right-hand man when Kissinger was secretary, is regarded by the Republican far right as a Trojan horse for Kissinger influences that they want to keep out of policy.

Increasing their concern is a belief that Walter J. Stossel Jr., slated to take the department's third-ranking post of undersecretary for political affairs, will hold the job only briefly before Eagleburger succeeds him.

Other Haig choices known to have incurred conservatives' ideological suspicion are John Holdridge (assistant secretary for Far East affairs), Chester Crocker (assistant secretary for African affairs) and Paul Wolfowitz (chief of the policy planning staff). In addition, Myer Rashish, scheduled to be undersecretary for economic affairs, has been questioned by the conservatives on grounds that they don't know enough about his views.

None of these appointments has been announced officially yet, and some sources speculated yesterday that they might be held up for a few days while Haig tries to make some conciliatory gestures toward the conservative. But, there also seemed little doubt that Haig has cleared his appointments with Reagan and, as a demonstration of his influence with the president, is determined to push them through whether the conservatives agree or not.

The selection of a deputy secretary of state apparently has been delayed by Haig's resistence to President Reagan's first choice, California Supreme Court Justice William Clark.

As recently as two weeks ago, Clark, who served as an aide to Reagan when he was governor of California, was telling interviewers that he had accepted the job, but no announcement has been forthcoming. Sources close to Haig say he believes that Clark is not qualified.

Several reliable sources said yesterday that one of the most sensitive unfilled posts in the department -- assistant secretary for Mideast affairs -- will go to Harry E. Bergold Jr., a career officer now serving as ambassador to Hungary and a protege of former energy secretary James Schlesinger. The job involves supervising U.S. policy with regard to the Arab-Israeli conflict, overseeing relations with the oil producing states of the Mideast and dealing with the volatile Persian Gulf region.

The only other key unfilled geographic-area job is assistant secretary for inter-American affairs. It reportedly has been offered to former Democratic senator Richard Stone of Florida, but he is understood to prefer an ambassadorship.