THE UNITED STATES may have pioneered grants for international educational exchanges as a foreign policy tool, but the Soviets and their satellites are running circles around us in this area today.

While exact figures are hard to come by, conservative State Department estimates indicate that 28,000 Third World students were in the Soviet Union and Eastern Europe in 1975. The figure climbed to 56,000 in 1979 and has reached about 63,000 today. The annual cost is conservatively estimated at $325 million.

By contrast, the total U.S. expenditure today is a mere $30 million, little of which goes to needy undergraduate students.

Neither Washington nor Moscow, of course, has entirely selfless motives in providing these scholarships.

The prestigious Fulbright awards introduced after World War II, for example, have funded graduate studies here for students from about 100 foreign nations, as well as for American students abroad. The result is that in a nation like Japan, the list of Fulbrighters reads like a virtual "Who's Who" of Japanese society -- ambassadors (34, including the current Japanese envoy to Washington), university presidents, editors, scientists and business executives.

Since 1960, the Russians have been appealing to the youth of Asia and Africa and -- poaching in America's traditional sphere of influence -- Latin America. While children of the elite in Nigeria, India or Colombia were studying at Oxford and the University of California, promising children of the poor, from remote villages or city slums, were being wooed by Moscow's recruiters.

They were offered free tuition, room, board, transportation, medical care and a small stipend for studies that would send them home as agronomists or doctors or mining engineers. The result, Moscow hoped, would be gratitude and admiration for the Soviet system -- and in some cases a more lasting attachment.

Indeed, State Department officials calculate that even if a majority of these students is turned off by the Soviet system, there is always a number -- perhaps one-third -- who return home committed communists.

The Russian challenge is most acute in Latin America. While the Soviets offered 400 grants a year there in the 1960s, the number jumped to more than 5,000 by 1980. The U.S. effort in the region that year? A total of 781 scholarships, with most of them renewals of existing grants.

As one discouraged official explains, it is no longer possible to make public announcements of Fulbright scholarships in Latin America. "It would simply be too embarrassing. What could we do if hundreds of people applied and then we were forced to say that there were only two or three scholarships available?"

The problem is not merely one of numbers. Moscow is appealing to an audience -- needy undergraduates -- that we, with relatively few exceptions, ignore.

The Fulbrights go to graduate students. Grants from the Agency for International Development help technicians who have spent years working for their own governments. Even the new program in honor of the late Hubert Humphrey is aimed at mid-career professionals who are brought here for a year.

Opponents of increased scholarships for undergraduates point out, quite accurately, that there are far more foreign students here than in the Soviet Union. At last count, there were more than 300,000 here, two- thirds undergraduates, 80 percent from the Third World.

But they come, increasingly, from comparatively wealthy countries -- 100,000 from OPEC nations alone. And even among those from poorer lands, the vast majority are from well-to-do families.

As Rep. Paul Simon (D-Ill.), chairman of the House subcommittee on postsecondary education, recently argued, "The masses on whom the future rests, and who do not know the United States as their wealthy cousins do, are the ones who need the education. Will we offer it, or will we default to the Soviets?"

In current budget circumstances, nobody can expect a burst of funding for such scholarships. But a modest amendment has been attached to the president's Caribbean Basin Initiative, and hopefully it will not disappear in Congress' lame-duck session.

Introduced by Rep. Michael Barnes (D-Md.), the amendment would earmark $7.5 million for scholarships for undergraduates from Central America and the Caribbean -- enough to allow 375 students to spend just two years at American colleges and universities.

While Congress has approved the Caribbean Basin funds, the House and Senate have not agreed on the details of the scholarship program. The problem is that the provision might well get lost in the haste of the current session, in which case the scholarship funds would be lost, lumped in with other AID projects in Latin America.

If this program becomes a reality in Central America, it could set a pattern for a worldwide program of undergraduate scholarships, at least as budget circumstances permit. That is no small matter, particularly to those who believe that the battle for the mind is critical to America's position and interests in the world.