The cost of the African policy now being pursued by the Carter administration is beginning to come home. It entails American support for black nationalists in violent confrontation with the minority white regimes of southern Africa.

But to what advantage? The evidence so far suggests that the administration stand has raised black hopes and hardened white resistance in a way harmful to this country's only serious interest: a peaceful resolution of the struggle.

In Africa, as in so many other places, the policy of the Carter administration defines itself by being different from that of President Nixon and Henry Kissinger. Nixon and Kissinger gave short shrift to black Africans and supported white-minority regimes in the Portuguese territories and in Rhodesia and South Africa.

That so-called "Tarbaby" policy reached a dead end when the Portuguese abandoned Angola. The rush to take over ended in a battle between one Angolan faction, backed by the United States and South Africa, and another faction, backed by the Soviet Union and Cuba. The Communist-supported faction won, leaviang the United States nakedly exposed as an ally of the South African whites in waht was - for the long run - a losing cause.

Secretary Kissinger drew the lesson and moved rapidly to switch the American stance. He put pressure on Prime Minister Ian Smith of Rhodesia to accept an international conference designed to achiefe a peaceful transition to majority rule in Rhodesia.

That principle won acceptance from Rhodesian black nationalists, the neighboring black governments and the segregationist regime of Prime Minister John Vorster in South Africa. Thus Washington, without being in confrontation with either Rhodesia or South Africa, made a transit to support for black-majority rule.

The Carter administration has thickened the commitment in several ways. The Presidnet and his leading subordinates - notably United Nations Ambassador Andrew Young - have given rhetorical expressionto the principle that support for black-majority rule in Africa is a test of the morality of American foreign policy.

The President and Secretary of State Cyrus Vance, in sessions with British Foreign Minister David Owen, have increased pressure on Smith of Rhodesia to move rapidly toward majority rule. Vice President Walter Mondale, in a meeting with Vorster in Vienna, made it plain that the United States expected South Africa, as well as Rhodesia, to begin moving toward majority rule.

The reaction of the white regimes has been to dig in against the pressure. Smith has long since reneged on his deal with Kissinger. He is now calling new elections for a mandate that would maintain white rule indefinitely in Rhodesia.

Vorster, in a speech last Saturday, served notice that he would no longer be an instrument for applying pressure on SMith to be reasonable. Vorster said American policy in southern Africa was following a course that "can lead only to one thing: chaos and anarchy."

African blacks have inevitably had their hopes raised by the Carter administration. The leading nationalist movements in Rhodesia have stopped negotiating with Smith and moved toward guerilla war. They have been supported in that posture by the heads of the neighboring black governments. Their position was spelled out with unmistakable clarity by President Julius Nyerere of Tanzania during a visit to this country last week.

After talks with President Carter at the White House, President Nyerere said he found Carter willing "to put on whatever pressures are needed in order to bring about majority rule." The Tanzanian president, who is perhaps the most prestigious leader in Africa, said: "Frankly, we have to escalate the war and we hope then; if President Carter and his allies can escalate their own pressures, these two escalations will shorten the struggle.

In oter words, a big smashup is in the works. The United States has aligned itself with the side that is morally right and that will surely prevail in the end. But how much is the American interest served by getting in the middle and catching the blame for the trouble ahead? Wouldn't it be better to stand slightly aloof, and be in position to help pick up the pieces after everything in southern African goes smash?