RADIO MARTI went on the air broadcasting to Cuba this week. It's a perfectly legal form of international communication. It addresses what is always the favorite American audience in a communist country, the people who make their own decisions on whether to tune in. It offers them a range of programming, including news about Cuba, that the controlled media do not provide. Congressmen who had earlier feared that this station would be too independent, provocative and strident had largely been reassured by changes made to bring Radio Marti under the umbrella of the long-established Voice of America.

Fidel Castro, himself a leading international broadcaster, lost his cool when Radio Marti opened. Without waiting to listen, he suspended last December's agreement under which immigration to the United States was to resume, and Cuba was to take back the misfits it shipped to the United States in 1980; he also halted Cuban-American travel to Cuba. Plainly, Mr. Castro could not abide that the station might break part of the monopoly he has tried to impose on the news fare available to his citizens. He knew how to react in a way that would cut at the limited personal choice that remains in Cuba and that would, therefore, pain Americans and build pressure in the American democratic system to kill Radio Marti.

With the Cuban sanctions -- they may not be the end, either -- there will be an argument between Washington and Havana and between the administration and its critics on this issue over whether President Reagan should have started up Radio Marti. We don't see how the United States can leave it to Fidel Castro to determine whether this country conducts a broadcasting activity that Cuba conducts and that is legal, open and politically valid. As a result of Mr. Castro's rage, some individuals will be hurt. That puts upon Washington a responsibility to do what it can politically to bring them relief. The fact is that the arbitrariness of the Castro response and its cruel impact on helpless individuals illustrate precisely the condition Radio Marti is meant to treat.

How? Notwithstanding some foolish early statements by this administration about going "to the source," the United States put aside the notion of unseating Fidel Castro decades ago. The Reagan administration's agreement on immigration last year illustrated its acceptance of the consensus -- to live with Mr. Castro -- that has prevailed since the Cuban missile crisis. Over the long haul, however, it is clearly in the American interest to see Cuba become governed in a more democratic way. This is more likely to happen if the public debate in Cuba is kept fresh by a project such as Radio Marti. No one has to listen who doesn't want to.