Richard T. McCormack, former aide to Sen. Jesse Helms (R-N.C.), has moved without announcement into a $50,000 consultant's role at the State Department, with a White House promise that he will be given the department's second-ranking economic policy job as soon as Myer Rashish quits the top-ranking State Department slot in that field.

In what will be a game of musical chairs that was set in motion three months ago, Assistant Secretary of State for Business and Economic Affairs Robert D. Hormats will move up to Rashish's position as under-secretary of state for economic affairs, the fifth highest slot in the State Department. McCormack, supported by conservative Republicans in the Senate, then will take over Hormats' job.

When the shift comes about, it will give conservative Republicans the broader base in policy-making at the State Department they have sought from the beginning of the Reagan administration. Helms initially fought the appointment of Rashish, a trade expert who had close links with the administration of President Kennedy.

Helms succeeded in delaying the Rashish appointment for a while, but not killing it. He was also suspicious of Hormats, whose career has spanned Democratic as well as Republican administrations.

It was publicly reported six weeks ago that Secretary of State Alexander M. Haig Jr. was planning to unload Rashish. But this has never been officially acknowledged, nor have the reasons for Haig's decision been made clear. A White House official told a reporter returning from the North-South summit in Cancun in late October that "I was surprised to see Rashish there, because I thought he was out." But as of yesterday, there still had been no decision on when Rashish is to leave, "because everybody wants to make sure that Mike gets out in one piece."

None of the principals would talk to a reporter for quotation, but it is clear that there are multiple embarrassments all around for Rashish and Hormats, who have been friends.

Since mid-August, the top bureaucracy at State has tiptoed its way around an awkward situation, acknowledging only that there is a "clash of personality" between Haig and Rashish. This has led to a degree of confusion among foreign economic officials, who fear that in dealing with Rashish, they are doing business with a lame duck.

Discussions of the "global negotiations" on Third World aid that were set in motion at the Cancun summit are now handled by Haig directly with Hormats and U.N. Ambassador Jeane J. Kirkpatrick, bypassing Rashish altogether.

There has been much speculation about why Haig is moving against Rashish. Some observers feel Rashish has been the victim of Haig's sometimes volatile swings of emotion. "Haig is up one day, down the next, and sometimes he doesn't seem to know his own mind," says a critic sympathetic to Rashish. Rashish may also have suffered from an unremitting effort by Helms to land a top job for McCormack.

Hormats, on the other hand, proved to be the right man in the right place at the right time. A veteran of all economic summits since the first in 1975, Hormats impressed President Reagan in personal dealings with his knowledge of foreign leaders and grasp of the issues in briefings prior to the Ottawa heads-of-state summit. And most important, he is considered a "team player" by the White House.

"Ed Meese and the rest of the top guys at the White House find it easy to deal with Hormats," said an informed outsider. "He didn't have that kind of base to start with, but he cultivated the relationships. Rashish had access only to President Reagan's national security adviser Richard V. Allen," who recommended him for the job.

McCormack gets mixed reviews from those who know the international trade and economic field. He is unarguably a free-market, liberal-trade exponent who will fit in neatly with the kind of do-it-yourself philosophy President Reagan offered to the poor nations at Cancun.

At one critical extreme, some Democrats think he has too little specialized experience to qualify for the job. McCormack himself claims only to be a "foreign-policy strategist" rather than an economic specialist. He has a B.A. from Georgetown University here, and a Ph.D. from the University of Fribourg in Switzerland.

Those who worked with him at the Nixon White House say "he is conservative, not an extremist, and those on the Hill looking for him to be an extremist may be disappointed."

McCormack went on the State payroll Wednesday, after serving as a volunteer, assigned to Hormats, for 30 days while on routine government clearance. Originally interested in becoming director of intelligence research at the State Department, McCormack was sounded out by the White House in midsummer on whether he would be interested in Hormats' job, when Hormats moves up to Rashish's.

The White House top staff, it was learned, had become convinced that the international economics set-up at State was "not working," and tended to blame Rashish. Rashish's problems may have started, according to observers here, with the president's first trip to Canada, when he felt that he had been inadequately briefed on bilateral economic problems that came up in the discussions with Prime Minister Pierre Elliott Trudeau.

Later on, White House officials reportedly complained that Rashish, who also had been named special representative for economic summits, didn't perform well at Ottawa. At the same time, Haig, whose first choice for the undersecretary post had been Hormats, also was becoming irritated with Rashish and wanted him out.

At the start, Haig and Rashish hit it off well. Urbane and witty, Rashish, as part of the Reagan transition team for State, drafted a plan for international economic policy-making that once again would put State at the forefront of the bureaucracy, taking over functions that the White House and Treasury Department had exercised. Haig liked it, and accepted Allen's recommendation of Rashish for the job.

"But Haig's style of managing," a high official said, "is for his subordinates to take an issue, develop all the angles, and then make sure it's carried out with a coherent set of objectives. Mike's style is to take an issue, provide a formulation of it, but not give as much time as may prove necessary for follow-up."

Late last spring, when the question of Japanese auto import quotas was being debated at top levels, the White House bypassed State to cut a "voluntary" deal with Japan which limited Japanese sales here. But Haig, uninformed, pursued the issue with former foreign minister Masayoshi Ito, whom the White House had promised that autos would be excluded from all his discussions. Haig apparently blamed Rashish for this goof, although Rashish apparently was just a surprised as Haig.

Haig, reportedly, does not discuss the present situation with Rashish, who has been looking around for another job. Meanwhile, Hormats, who must clear roughly half of his business with Rashish--the rest of his dealings are either directly with Haig or other undersecretaries--does not discuss the prospective succession with Rashish. Although he had been at State for 30 days, McCormack was officially introduced to Rashish for the first time on Wednesday.

Haig would have been willing to nominate Rashish as Director General of the Organization for Economic Cooperation and Development in Paris. Rashish explored this prospect with European nations, but they made it clear that the OECD post should be reserved for a European.

Rashish has rejected the only other administration posts that have been opened to him -- U.S. executive director to the World Bank (a sharp reduction in status) and ambassador-at-large within the State Department.