Current congressional moves toward economic sanctions against South Africa offer evidence of what a band of dedicated activists can accomplish when it knows how to attract and rally public opinion.

On July 11, the Senate voted 80 to 12 for a bill banning new bank loans and exports of nuclear technology to South Africa, and requiring American companies with interests in South Africa to take an active role in opposing its apartheid policy of racial segregation.

The legislation is seen by many as sending a strong message to Pretoria and to the Reagan administration, which continues to oppose sanctions while adhering to a policy of "constructive engagement" with the South African government.

In June, the House voted 295 to 127 for a tougher measure that also would halt importation of krugerrands into the United States. Last year $600 million worth of those South African gold coins were sold to Americans, more than half the total exported. One-third of the Republicans joined almost all the Democrats in the House vote.

The bills are now in Senate-House conference, and what will emerge is not certain. But what does seem apparent is that there would have been no action at all except for the work over the past eight months of a group known as the "Free South Africa Movement."

The group began picketing near the South African Embassy in Washington last November, protesting the jailing of a number of labor leaders. The protests drew a good bit of television coverage, and similar protests sprang up in other cities.

After 16 days, the labor leaders were released but the picketing continued, shifting focus to the larger problem of apartheid. Emerging as a spokesman for the movement was Randall Robinson, the executive director of a foreign policy lobby, TransAfrica.

By last week, 2,900 people had been arrested in Washington and more than 4,000 at demonstrations at 26 other cities or college campuses.

So far, 22 members of Congress have chosen to be arrested and so have a number of mayors, and union and religious leaders. The most recent celebrity arrest was that of Coretta Scott King, widow of a slain civil rights leader. The picketing takes place every weekday, and Robinson is not yet short of pickters. On holidays like Mother's Day, there has been Sunday protesting as well.

Herbert Beukes, South Africa's ambassador to the United States, contends that his government will not be intimidated by protests "half a world away," and says the motives of Robinson's group are domestic, political ones.

Whether or not that is true, the activists' domestic success is beyond dispute. Aside from the large number of arrests and congressional action, evidence gathered from two Washington Post-ABC News opinion polls shows growing support for the protests.

In January, when the protests were two months old, the Post-ABC News poll asked a random sample of Americans if they had heard about the picketing in Washington and elsewhere. About half (52 percent) said they had. Among them, 46 percent said they approved of the protests and 21 percent said they opposed them.

In mid-June, the Post-ABC News poll found a 10-point increase in the number of people aware of the protests, up to 62 percent. Among that larger group, virtually the same proportion as in the earlier survey -- 46 to 22 percent this time -- said they approved.

In June the survey also showed a strong relationship between public support for what Congress was doing and awareness of the protests.

The poll put this question to the public:

"Congress is working to take economic action aimed at forcing South Africa to end or reduce racial segregation. Reagan opposes such economic action, saying it would not help the situation there. Whom do you tend to side with, Congress or Reagan?"

Overall, the public was about evenly divided, with 46 percent siding with Congress, 44 percent with Reagan and 10 percent undecided.

Among the 38 percent who had not heard of the protests, 49 percent supported Reagan's view, 40 percent Congress'.

Among the 62 percent who had heard of the protests, 50 percent sided with Congress, 41 percent with Reagan, 9 percent were undecided.

Robinson sees three factors that have propelled the economic sanctions to the threshold of congressional enactment. Together, they serve as a model for any activist movement.

First is consistency. "The people involved are prepared to go on as many months or years as necessary," Robinson said.

Second is what Robinson called a consumable message. "We felt that if we could put the message before the American people, they would make the right decision. The issue is what is fair and what is unfair."

Third is hard lobbying. "Congress has to be lobbied from within," he said, and the protests and "other kinds of public pressures are needed to make them more responsive."

Asked whether there would have been any legislation at all if not for the embassy protests, Senate Majority Leader Robert J. Dole (R-Kan.) said, "Well, it focused on the problem. And I think from that standpoint, those who had the responsibility, [Senate Foreign Relations Committee Chairman] Richard G. Lugar R-Ind. and others at the hearings, made modifications.

" . . . Not only the focus, not being arrested and all that, but the fact that they were very actively visiting the different people on the Hill. Let's face it: Some see it as a big civil rights issue that's important down the road . . . . All that has an impact."