They're playing musical chairs in the White House, but one of the players doesn't like the rules.

Midge Costanza, until recently President Carter's highest ranking woman assistant, is resisting an order to vacate her prestigious spot just down the hall from Carter's Oval Office and move across the street to the Executive Office Building.

Costanza has told the president's chief political adviser, Hamilton Jordan, that she will move out of her office, probably by the end of the month. But she is insisting that she be relocated not in the bureaucratic hinterland of the Executive Office Building but in another office in the White House West Wing, where the most senior and powerful presidential aides reside.

It is not her status that she is worried about, Costanza said yesterday, but a question of preceptions in this power-conscious city. She said she fears a move across the street would be viewed as a sign that her areas of responsibilities - chiefly women's issues and domestic human rights - are not important in the Carter White House.

Moving Costanza out of the office she has used since Jan. 20, 1977, is part of the White House staff reorganization that has been engineered by Jordan.

It is the messy part, involving actions that affect the egos, feelings and status of people at the highest level of government.

Costanza, an outspoken and feisty former vice mayor of Rochester, N.Y., has never been a part of the Carter inner circle. Periodically reports have said she has annoyed the president's most senior aides from Georgia.

Through all this, Costanza has maintained her title - assistant to the president for public liaison - and her $56,000-a-year salary.

But she now shares the distinction of being the highest ranking woman in the White House with Anne Wexler, a former deputy under secretary of the commerce. Wexler joined the White House staff last month in the first of the moves instituted by Jordan.

Although Wexler took over many of Costanza's public duties, Costanza was not told of the change in advance. And if office space and location are symbolically important, Wexler's status was established when she moved into a West office once occupied by Energy Secretary James R. Schlesinger Jr.

Schlesinger, no slouch himself at protecting the symbols of bureaucratic importance, resisted giving up that office even after he had left the White House staff and become Energy Secretary. For months, he was the only Cabinet secretary who had an office in the White House.

Now it is Costanza's office, strategically located between the Oval Office and Jordan's office, that is at stake.

Costanza was informed of the impending space shift in a memo from Jordan sent early this week while she was in California. "We made some decisions," Jordan said in the memo, leaving little room for argument.

Jordan informed Costanza that she would move to the Executive Office Building and that her office would be occupied by Tim Kraft, raft was Carter's appoinments secretary, with a small office nestled next to the Oval Office. But he has been promoted to the senior staff to work on political matters with Jordan. Jordan wants him nearby, specifically in Costanza's office.

Costanza, however, has never been shy about arguing back.

"I am not under siege," she said yesterday, explaining that she went to Jordan with her argument about the importance of her issues and the symbolic damage that would be done if she shunted across the street.

"It's the importance of the issues,"she said. "It's not me, I can work anywhere."

Costanza said Jordan "understands" and promised to do what he could to find another office for her in the West Wing.

That is where the White House game of musical chairs now stands. Wexler is firmly ensconced in Schlesinger's old office. Phil Wise, the new appointments secretary, is in Kraft's old office. Kraft is over in Wise's old office in the Executive Office Building, waiting for Costanza to move. And Jordan presumably is looking through the West Wing for a place for Costanza.