THE IDEA OF A TAX on imported oil keeps turning up, no matter how firmly the administration's austere free-marketeers try to repress it. This time the free-marketeers are right. But with the price of oil hovering around $10 a barrel, a sense of real desperation is spreading among the producers. In the absence of any better suggestion, a tax on imports is the cause to which some of them -- although not all -- now rally.

Like any tariff, a tax on imported oil is a device to raise domestic prices. But there would have to be some exceptions to a tariff on oil. Canadian oil certainly would not be taxed. This country is currently preparing to negotiate a free trade agreement with Canada. What about Mexico? The falling price of oil has already disrupted the Mexican economy severely, and surely no one in Washington wants to increase the pressure on a close neighbor already in financial trouble. If Mexican oil is exempted, it would be very hard not to give equal treatment to Venezuela, a reliable supplier over many decades. But if Venezuela is exempted, how about Britain? And Nigeria, a country with an income per capita one third Mexico's, which is also suffering greatly from the fall in prices? And if poverty is a consideration, as it certainly should be, should there not also be an exemption for Indonesia, far poorer even than Nigeria?

There you have the six countries that are the leading oil suppliers to the United States, together accounting for about 60 percent of the oil that came into this country last year. The tax on imports enjoys much support among people who think of it as a way to punish the Arab exporters for their oil embargo 12 years ago and all their transgressions since. But as an instrument to chastise the Arabs, the tax would hardly be eive. Only about 10 percent of this country's oil comes from the Arab countries. A tax applied only to Arab oil would have little impact on either prices or volumes of the exports coming into this country.

If prices remain down in the present range for long, American oil production will certainly be hurt. Exploration has already fallen off drastically. Unfortunately, there isn't much that the federal government can do about that. The oil industry seems to have entered a period of radical instability.

As a minor but helpful interim remedy, the Reagan administration might want to reconsider its decision to stop buying oil for the Strategic Petroleum Reserve. Having bought half a billion barrels of oil at prices frequently over $30 a barrel, the government should not lightly pass up an opportunity to buy at $10. It would be a modest kind of price-support mechanism and, unlike the grain reserves that the government buys for the same purpose, it would be valuable insurance against another of the shortages that the country has suffered twice since 1973.