One of the most controversial proposals President Carter is contemplating to fight inflation -- a fee on imported oil -- would increase prices in the short run, rather than reduce them.

Administration officials backing the fee have proposed that its full effect be felt on gasoline prices. If that were done, each $1 a barrel in fees would mean a 2.5 cent-a-gallon increase in prices at the pump.

A $4-a-barrel fee -- about the amount Carter is said to have under study -- would raise gasoline prices about a adime a gallon. That would boost the consumer price index by about 0.4 percent immediatley and perhaps double that amount as the higher cost of gasoline to business began to be reflected in prices of other goods and services, one expert esitmated yesterday.

But at least some administration experts say the fee eventually would help restrain inflation in three respects. First, the income would help balance the budget. Second, the higher prices would help wean Americans from gasoline and therefore from costly imported oil. Third, reduced energy consumption would help fend off future world oil price increases.

Carter has the power under trade laws to impose an import fee, as President Ford did for several months in 1975, without congressional approval.

The fee would raise directly about $2.5 billion in new revenues for each $1 a barrel in fees. That money could help balance the 1981 budget.

The fee also would bring so-called sympathetic price increases for domestic crude oil that is free of price controls. Through the workings of the crude oil tax pending in Congress those price increases would add several hundred million dollars more to federal coffers.

Carter's top economic advisers have asked their staffs to update fee analyses first done last December when the administration was seeking possible ways to cut gasoline consumption in 1980.

The fee idea was rejected then officials such as Energy Secretary Charles Duncan said, because the Organization of Petroleum Exporting Countries was sharply boosting the price of oil, and those higher prices were expected to cut gasoline use. In such a rapidly changing situation, the officials said, it was all but impossible to decide how much higher prices needed to rise to meet any given conservation goal.

Since then, gasoline and other petroleum product prices have risen faster than administration energy experts expected, and consumption is down sharply.

Gasoline use in February was down nearly 8 percent compared to last year, though the 1979 figures may have been inflated somewhat as many gasoline users stocked up in fear of what effect the Iranian revolution would have on supplies.

Overall oil dropped more than 10 percent. With the aid of a milder-than-normal winter distillate fuel oil use -- which includes home heating oil and diesel fuel -- fell almost 19 percent.

Gasoline and crude oil stocks are at record levels and home heating oil inventories are nearly 50 million barrels, 51 percent above a year ago.

The global oil supply and demand picture is not much different, with stocks rising in almost every major industrial country and production running well above use.

However, some economists believe the greatest single danger to any Carter administration anti-inflation effort remains the possibility of further OPEC oil price increases. Even with plenty of slack in world oil markets for the moment, any interruption of supplies might set off another round of price increases, the argue.

Therefor, any steps that might cut U.S. oil consumption -- particularly if other industrial nations could be persuaded to cut their oil imports as well -- would improve the odds against another price increase.

Some economists, including Barry Bosworth of the Booking Institution, have suggested that gasoline rationing would provide an even larger margin of safety against higher oil prices. But top officials consider rationing unworkable, and the administration is not condsidering it.

The analyses on the import fee also raised serious questions about whether it would work, especially on any attempt to force refiners to pass the fee on only through gasoline prices.

Backers of the fee believe the entitlements program -- a system of payments among refiners intended to roughly equalize their crude oil costs even though some have access to cheaper, price-controlled domestic crude -- could be used to force refiners to apply the full fee to gasoline prices or absorb it themselves and accept lower profits.

But the entitlements program is supposed to vanish along with price controls on domestic crude oil and gasoline at the end of September 1981. At the point, there would be no mechanism available to the administration to keep the fee from affecting the price of other products, including home heating oil, which Carter officials want to avoid.

The alternative, at least on paper, would be for Carter to propose an increase in the federal excise tax on gasoline to replace the import fee. That would require approval of Congress. But if there has been any discussion of proposing a gasoline tax increase, Carter's advisers have kept it to themselves.