White House Chief of Staff Howard Baker is showing his stuff. The other day, he explained the administration's Persian Gulf policy in terms that can only be called silly. He sounded like Richard Nixon, circa 1946, campaigning for his first House seat. Once again -- and this time for less reason -- cliches about the Soviet threat substituted for serious thought.

The lead, as journalists call the first and most important paragraph, was that the United States might withdraw its warships from the Gulf if the Soviets did the same. But having said something sensible, Baker then turned to anti-Soviet boilerplate: The United States would not ''cede control'' of the region to the Soviets, the Gulf must not become ''a Russian lake,'' and freedom of the seas must be maintained.

The trouble with these statements is not that they are not true, but that they have little to do with the situation in the Persian Gulf. Freedom of the seas is always a worthwhile principle, but it is not at stake in the Gulf -- especially where the United States is concerned. With one exception, our ships have not been attacked, and the one that was -- the USS Stark -- was hit by our new-found buddy, Iraq, and then by accident. The Iranians have been scrupulous in avoiding U.S. ships. On the other hand, Russian tankers have been among the ones attacked.

As for ceding control of the region to the Soviets and allowing the Persian Gulf to become their lake, there is not the remotest chance of that happening. The Soviets are not trying to push the United States out of the region and, in fact, they have suggested a reduction in military activity. It was the Kuwaitis who asked to charter Soviet tankers and it was the United States which responded in something of a panic -- an offer to ''reflag'' 11 Kuwaiti tankers.

The trouble with Baker's rhetoric is that it is excessive. It alerts us to a threat that is not there and ignores the one that is. The concept of a Soviet or even U.S. lake is dated. It conjures up a world that existed only immediately following World War II, when American power was thought to be absolute (it really wasn't) and we moved to replace the British as the nanny of the Third World.

But the Soviets are also a superpower, and their relationship with Kuwait is a well-established one. In 1979, Kuwait started to receive Russian arms, including missiles; just three years ago it concluded yet another arms agreement with Moscow. The Russians have had a toe in this lake for some time. It's absurd to talk now about keeping them out.

The real threat to the United States in the Gulf region is the chance that we might be drawn into the Iran-Iraq war. By coming to the aid of Kuwait, we have sided with an Iraqi ally -- a shifty one which has proved itself adept at playing one superpower off against another. The Iranian response is not likely to be an attack on an American vessel but, instead, an upsurge in terrorism. As in Vietnam, we may find that our power cannot be applied.

Much of our Gulf policy is inexplicable. The Iraqis started the war, yet we side with them. They initiated the so-called tanker war, yet we threaten the Iranians. Our oil supply is not at stake, yet we act as if it is, while Western Europe and Japan, for which Gulf oil is essential, seem hardly concerned at all. Among other things, the world's major oil importers know that their lifelines are not threatened.

The country in a mild panic is the United States. It has rushed naval ships to the Gulf to defend the hoariest of doctrines -- keeping the Soviets out of where they in fact already are. In the mouth of Howard Baker, contemporary complexities and realities are enunciated in the cliches of yesterday and, in the manner of Congress, contradictions are resolved by ignoring them.

When it comes to foreign policy, the administration seems to have chosen the perfect spokesman. Baker says what he means, even if what he says has little meaning at all.