PRESIDENT REAGAN has been on a kind of summer offensive, trying to convince groups of voters that he understands and sympathizes with their concerns. The first target was blacks, then women, then those who have trouble getting enough food. The next group to be wooed, the White House is making no secret, is Hispanics. Vice President Bush was in San Antonio this week, speaking to the National Hispanic Voter Registration Conference, in a preview of a series of speeches and events aimed at Hispanic voters--and nonvoters who may become voters by November 1984.

The Republicans are not conceding all the Hispanic vote to the Democrats. They argue that Republicans represent better than Democrats "the Hispanic values of family, neighborhood, church, freedom, and opportunity." They argue that their economic policies will bring the sustained prosperity Hispanics need to get ahead. And they accuse the Democrats of taking Hispanic voters for granted.

The Democrats argue that they deserve Hispanic votes because their policies would reduce unemployment (which is 12.3 percent among Hispanics, compared with 9.5 percent generally) and would support programs that help Hispanic voters directly. The number of Hispanic voters is increasing, and efforts are now being made to add 1 million to the 3.5 million Hispanics registered to vote out of 6 million. The Democrats hope that the lion's share of these votes will be theirs. But the Republicans are not conceding them, and with some cause.

For no one can be sure how these voters will respond to the choices of the next several years. The word "Hispanic" itself is nothing more than a convenient way to refer to a large number of diverse groups that have in common, now or somewhere in their past, a Spanish language heritage. The Cuban-Americans of South Florida are strongly anti-Castro and vote heavily Republican; there is evidence that many recent Central American immigrants are strongly anti- Communist, and they may end up as Republicans too. Puerto Ricans vote overwhelmingly Democratic, but their turnout in mainland elections is low, in vivid contrast to the high turnout in elections in Puerto Rico; they, like many other Hispanics, seem more interested in the politics and culture of their native land than in the politics of the place where they have, for the time being, found work. Mexican-Americans vote overwhelmingly Democratic in some elections, but not necessarily in others.

This nation's Hispanic population has increased dramatically since 1970, and the circumstances in which it lives are changing all the time. So it makes no sense to suppose that these voters' partisan preference will be static. Concentrated in big electoral states like California, Texas, Florida and New York, they will receive plenty of attention from politicians over the next year. It will be interesting to see to what extent the different visions of America presented by Republicans and Democrats will appeal to the diverse body of voters we call Hispanics in 1984 and after.