IT IS A SHABBY GAME the United States is playing with Ian Smith, prime minister of Rhodesia, over his attempt to visit the United States. Invited two weeks ago by friendly senators to present his case for more American support, he was expected to arrive this week. But the State Department, otherwise the champion of an open visa policy, has so far refused him permission to come. Why?

The State Department says that to honor Mr. Smith's Rhodesian passport would violate the sanctions voted against his "illegal" government by the United Nations. Yet the passports of Rhodesian students are regularly accepted, and the legal loophole of "exceptional humanitarian grounds" surely fits a visit by someone trying to end a bitter war. Must the United States be "purer" than Zambia, which has several times admitted Mr. Smith? President Carter himself has suggested giving him a tourist visa, which would not imply recognition of his regime. But the State Department, claiming that a visit now would determine "delicate negotiations," defers decision. Thus does it nourish the suspicion that it wishes to keep Mr. Smith from expanding the ranks of those who feel that the American aim is to promote a guerilla victory.

Yesterday, news reports indicated that the State Department might consider granting a visa if Mr. Smith agreed to attend the administration's longsought all-parties conference. If it is all right for the Department to try to win Mr. Smith and his black colleagues in Salisbury to the American course, then Mr. Smith should have the reverse opportunity. And if the department wants to practice persuasion, let it simply co-sponsor the senators' invitation. After all, more than a visa is involved. The main reason the Salisbury government has resisted American policy is its fear that the United States is too committed to pleasing certain countries in black Africa to give a moderate government with whites in it a fair shake. That fear is only confirmed by the visa shell game.

Finally, one must ask how it looks to the guerillas to see the United States treating Ian Smith like dirt. The other day the guerillas shot down a civilian Rhodesian airliner and then murdered some survivors of the crash. Does not the diplomatic gesture reinforce the atrocity by proclaiming white Rhodesians pariahs who somehow exist outside the bounds of ordinary civilities? This is a desperate time in Rhodesia-a time to give first priority to halting a war that threatens tragedy for blacks as well as whites. That means, in this instance, showing Ian Smith-and everyone else in Rhodesia/Zimbabwe-that the United States has the whites' legitimate interests at heart. That is what the visa question is really about.