MIAMI BEACH -- Republican presidential contender Pat Robertson has hitched his campaign in the South to a Soviet missile, a strategic gamble designed to turn a political lemon into lemonade.

Although he concedes that his controversial -- and so far, unsubstantiated -- claim that the Soviets have a nuclear missile installation in Cuba contributed to his last-place finish in the New Hampshire primary, Robertson has revived the charge here in the South as he seeks votes from Cuban Americans and other strong anticommunist groups in the upcoming southern primaries.

"The Cuban {missile question} is a major issue that must be taken to the American people," Robertson said Wednesday, shortly before he addressed a boisterous rally of Cuban Americans in a ramshackle hotel in the Art Deco district on the beach here.

Robertson surprised all the GOP contenders in last weekend's New Hampshire debate when he announced that he had received information that the Soviets have intermediate-range nuclear missiles in Cuba aimed at the United States. The assertion briefly became a hot campaign topic.

The White House issued a formal statement saying Robertson was wrong. For the other Republican candidates, the missile issue provided the chance they've been looking for to attack the former television evangelist without risking charges of religious bigotry. They said the unproven claim shows that Robertson is "rash" and "ill-informed."

Robertson initially backed off his charge, arguing that he was merely raising a question as to whether there might be such missiles in Cuba. On primary Tuesday, he acknowledged that the voters in New Hampshire "might not like what I said about the Cuban missiles."

But as the candidate and his entourage left New Hampshire, Robertson's Florida campaign staff told him the missile issue rang out loud and clear in Miami, particularly in the politically active Cuban community.

Robertson is now saying that the Reagan White House should demand the right to search Cuba to determine whether nuclear missiles are there. He said the president should reopen negotiations on the Intermediate-Range Nuclear Forces (INF) Treaty to include a clause banning such missiles in Cuba. The lack of such treaty language, he says, is "a big Cuban loophole."

The strategy is a risky one. For one thing, it puts the conservative candidate on the wrong side of the conservative president. For another, Robertson has had a difficult time deciding exactly how strongly to assert his charge. Since he left New Hampshire early Wednesday, he has gone back and forth.

At one point he said he had documentation and witnesses; he promised to make the documentation public. Asked again three hours later, he hedged and said "I have no first-hand knowledge." But when a reporter here suggested he could not prove his claim, the candidate responded hotly, "I am not backing off from it at all."

Robertson's dalliance with the missile question reflects a continuing problem that has dogged his campaign. He tends to make unequivocal assertions that he is unable to substantiate. Reporters covering Robertson refer to these statements as "funny facts."

Robertson has said he knew of a man who got AIDS by kissing his wife, he knew of a preschool child who takes drugs, that children in Iowa had been prohibited from saying "Merry Christmas" in public school, and that Japan requires TV commercials for American products to be broadcast in English. In each case, Robertson conceded there was no proof for the claim, but he continued to say he was right.