THE ELECTION of a black prime minister in Rhodesia puts American policy in a crack. To reject the election, because it was held under a constitution giving whites special privileges, dismisses the impressive participation by a black majority and invites guerrillas to flout the people's will. Yet to embrace the election is to assure continuance of a war that will pose a merciless test to the fledgling regime. Lifting sanctions would do little good if, as is likely, the United States does not then offer the major support essential to keep the new government afloat.

There may be no satisfactory way out of this dilemma, as long as it is posed in those terms. Policy then becomes just a test of political strength; for neither side can this be a happy prospect. That is precisely the appeal of the approach being taken by Allard Lowenstein, old Africa hand, former congressman and Carter-administration diplomat, and an observer of the recent elections. In an unorthodox yet promising initiative that reached the public in his House testimony yesterday, he has been exploring a way to free the Rhodesia debate from the sterile confrontational framework of the last year.

Mr. Lowenstein wants an American "all-parties conference," that is, an American consensus on the goal of Rhodesia policy. He sees that goal as establishing and securing the democratic process in Rhodesia with the least possible bloodshed. It follows that the recent elections would be regarded as an authentic and valuable statement of the people-not necessarily as endorsement of the constitution as it stands or of the Muzorewa government specifically, but of the replacement of war by the electoral process as the way to determine the country's future.

If it is understood that this is primarily what blacks were voting for, suggests Mr. Lowenstein, it becomes possible to ask what further steps might be taken to bring about by political means the genuine transfer of power to blacks that black nationalism and American law alike require. Such steps might include: a demonstration by Bishop Muzorewa, once in office, that his government actually serves black interests; submission of the constitution, with amendments, to black voters (only whites have voted on it so far); and negotiations, leading to further elections, with the Patriotic Front.

Mr. Lowenstein is an operator, both in Washington and in Africa, and the administration, while respectful of his credentials, has kept its distance. Yet he would seem to be offering the administration an approach that could ease its battle with its American critics and serve its own Africa goals more readily than its own excessively rigid policy now promises to do. At the least his views deserve full debate.