Jimmy Carter has a powerful case against the actions of Cuba in Africa. But by overstating the evidence of secret intelligence, he has allowed the case to be muddied and trivialized by Fidel Castro and by members of the Congress and the press.

Now the American position in Africa has to be restated anew in full perspective. That task devolves upon Secretary of State Cyrus Vance, and provides an interesting test of whether he is truly equal to the commanding role his many well-wishers have been staking out for him.

The case against Cuba is written on the map. It is a tiny island with less than 10 million people. It normally figures in world affairs only as a producer of sugar. It lives next to a superpower with security responsibilities that girdle the globe.

Common sense dictates that the Cubans should be careful not to put their finger in the American eye for less than vital reasons. The careful behavior of Finland toward its neighbor the Soviet Union is the appropriate model for Cuba and the United States.

But in Africa, where he has no vital interest, Castro has been systematically sticking it to the United States on behalf of the Russians. Cuban troops, ferried to Africa by the Russians, backed an anti-American faction in the Angolan civil war and now maintain that group in power by the presence of 20,000 men.

The Cubans have equally provided the military manpower, 17,000 troops, that maintains the Soviet presence in Ethiopia. Worse still, if the projected Anglo-American plan for a Rhodesian settlement breaks down, the Cubans may be pitched into a civil war in that country.

They would then be lined up with African states and radical black Rhodesians in a fight against Rhodesian whites and moderate blacks. The Cubans would thus be acting as surrogates for the Russians in a racial war acutely embarrassing to the United States.

To be sure, the American case in all these matters is far from perfect. This country, largely because of loyalities to the corrupt regime in Zaire, chose to support a losing faction in Angola. It backed Somalia, which was the aggressor in the fighting that brought the Cubans into Ethionia. It has raised black hopes in ways that increase the likelihood of civil war in Rhodesia.

But whatever the American faults, the Cubans simply had no business in Africa at all. They have been acting as proxy for the Russians with intentions clearly inimical to the United States. That is an unwise and dangerous policy, and Carter had every right to lay it on the Cubans when an invasion from Angola threatened the dismemberment of Zaire.

Unfortunately, the President, instead of stating the general case, made a specific allegation based on secret intelligence. "We," he said at a news conference in Chicago on May 25, "know that the Cubans have played a key role in training and equipping" the forces that attacked Zaire.

In fact, the evidence is far from clear Castro has denied the charge and given American congressmen a story to the effect that Cuba actually tried to block the invasion from Angola. Since then certain elements of the Congress and the press have had the field day they always have when a president is caught saying something he cannot prove.

Almost everybody is now confused, and some part of the public must have the incorrect impression that Carter is wrong and Castro right. What is required is a thorough exposition of American policy in Africa. Vance has undertaken to make it in a speech Tuesday in Atlantic City.

It is a tall order. Vance will have to square American policy in Africa with this country's global interests vis-a-vis the Soviet Union. He will have to explain particular actions in Angola, Zaire, Ethiopia and Rhodesia. He will have to show that a relatively conciliatory position in Africa does not mean a cave-in to Russia around the world.

But it is a fair test, given the rivalry between the secretary and the president's chief White House adviser on foreign policy, Zbigniew Brzezinski. Those who doubt Brzezinzki's judgment primacy to Vance. The president seems to be moving in that direction. But even the secretary's strongest supporters have to ask themselves a question that will come up for testing in the Atlantic City speech. The question is whether Vance actually has the qualities required for giving the president the guidance he needs in foreign policy.