THE most visible vacancy President Reagan has to fill as he moves toward his second inauguration is the United Nations ambassadorship Jeane J. Kirkpatrick is evacuating.
If the President wants to go into the history books as a peace president who reduced nuclear arms, as this columnist has firmly believed for the past two years, he would do well to fill that vacancy with care.
Mr. Reagan has made the right moves in upgrading the role of missile negotiator Paul Nitze and giving Secretary of State George P. Shultz primacy in directing the arms control team. If he now appoints a first-rate professional to the UN, he will do much to shore up world perceptions of what his arms negotiators are doing. Whatever the UN's deficiencies, it still is the place where future prime ministers and foreign ministers of the world go to finishing school. It is the place where many world leaders come to meet each other every fall. And it is also the home of much of the third-world suspicion that the superpowers are performing a self-serving shell game when they negotiate on arms.
Mrs. Kirkpatrick's departure is stirring up a lot of attention because followers of her neo-conservative banner would like to persuade Reagan to change his mind and find a suitably important post for Ambassador Kirkpatrick.
That has left the equally important question of Kirkpatrick's successor almost a forgotten issue.
One reason is that public interest in the US ambassador and in the UN itself has dwindled in the nearly 40 years since the organization was founded to keep world peace, after the biggest (and first nuclear) war in history.
If you were out of school by the beginning of the '50s you are likely to recall these TV vignettes which made the American UN ambassador if not a Tom Selleck, at least an equal of Walter Cronkite:
* Warren Austin pleading with Israelis and Arabs to seek peace ''like Christian gentlemen.''
* Adlai Stevenson, uncharacteristically pugnacious, threatening to wait for Moscow's answer on Cuban missiles ''until hell freezes over.''
* Charles Yost casting the first American veto in the Security Council - a role previously dominated by Soviet delegates.
The only recent capsule event suitable for television's 30-second memory lane came in 1983 when Jeane Kirkpatrick's deputy, Charles M. Lichenstein, told the Security Council that if the UN wanted to leave New York he would be happy to be ''at dockside bidding you a farewell as you set off into (sic) the sunset.'' (That bit of hubris would have been roughly equivalent to waving farewell to the Titanic just before an iceberg sank the dock on which he stood.)
Reagan and his aides ought to pick a new ambassador with history, not domestic politics, in mind. It's true that the post has conferred little power since Warren Austin and Henry Cabot Lodge had the ear of the president and on occasion made policy on their own.
Reagan might choose one of the GOP internationalists currently out of politics. For instance, outgoing Senate Foreign Relations Committee chairman Charles H. Percy, former multi-Cabinet secretary Elliot Richardson, or retiring Senate majority leader Howard H. Baker Jr. (who might be persuaded to take the job for a couple of years to add to his foreign policy credentials as a presidential candidate).
Realists would scrub all three: Mr. Percy because he's likely to become ambassador to India; Mr. Richardson because he helped craft a Law of the Sea treaty the administration spurned and was at odds with the GOP convention; Mr. Baker because he would be hard to recruit. All three would be likely to draw opposition from the far right wing of the GOP.
If the President wants to skirt that kind of battle, he could replace Kirkpatrick with one of her admirers, such as Boston University president John Silber. He recently passed muster at the White House while being screened for the secretary of education job. He would bring to the job intensity of effort and strong administrative skills. The human race has an unfortunate tendency to scare itself into constructing peace machinery after major wars, then letting the machinery fall into disuse when it doesn't work exactly as prescribed. The Congress of Vienna, League of Nations, and now the UN suffered from gradually shrinking interest.
Reagan's predecessors after President Eisenhower did little to arrest this trend. ''Realists'' do not expect Reagan to start a reversal. But then those realists did not expect the President to be serious about arms reduction, either.
If the Reagan years are to be known to future history students as years in which the economic system of the US was altered and in which the arms race turned downward, an articulate voice at the forum of nations - speaking for both free enterprise and peace - would be useful. Reagan understands symbolism and visibility at home. He could use more of the same on the world scene.
Earl W. Foell is editor in chief of The Christian Science Monitor.