In an attempt to reassert executive prerogatives, President Reagan soon will approve the sale of Stinger missiles to the tiny state of Bahrain, despite threats of a legislative ban.

Frank Carlucci, while still serving as national security adviser before becoming secretary of defense, signaled the decision Nov. 20 in a candid letter to Senate Minority Leader Robert Dole. Carlucci warned that refusal to heed Bahrain's request would find the Soviet Union ''more than ready and able'' to supply hand-held anti-aircraft weapons similar to the Stinger.

The administration's greater purpose here is to prove the United States, so often forced by Congress into covert operations to help its friends, can still assist them with open military aid. ''We're hanging by our fingernails in letting the world see that we can project power,'' one Reagan policy maker told us, ''and that has to change.''

This incidentally pits the lame-duck administration against the bipartisan pro-Israel bloc in Congress, which claims the Stingers sought by the pro-Western Arab state for air defense against Iran might wind up in hostile Arab hands. In the past, President Reagan has retreated under such pressure. But since the amount of money involved is only a few million dollars, both houses of Congress would have to pass the ban and be subject to a veto. That makes the issue worth a test of presidential authority.

Two leading supporters of Israel, Democratic Reps. Lawrence J. Smith of Florida and Mel Levine of California, won a lopsided House vote last week to block the sale. They did so despite an appeal from Rep. Stephen J. Solarz of New York, a senior member of the House Foreign Affairs Committee. His support for the sale (he called ''sheer hogwash'' claims that the Stingers would abet terrorism) marked a rare split in the the pro-Israel bloc, where Solarz is a major figure.

Congressional micromanagement has crippled U.S. use of arms shipments in the national interest. Congress first froze the administration out of overt military help for anticommunist fighters in Nicaragua, then covert aid too. The president is limited to covert aid for anti-communist guerrillas in Angola and Afghanistan.

Against that background, the White House views the moderate Arab states -- Saudi Arabia, Jordan and Bahrain -- as a staging ground for a comeback. It hopes that open arms shipments to friendly countries can project to the world an image of military power and self-assured diplomacy.

The effort has flopped in Jordan because of its proximity to Israel. The pro-Israel lobby controls all the levers of U.S. policy toward that formerly close American ally, which has been steadily forced away from its U.S. connection. Jordan is now bargaining for large-scale military help from Moscow, which eagerly solicits new Arab allies.

But Saudi Arabia and Bahrain are turning into conspicuous successes in the administration's attempt to project power. Thus, though the most recent Saudi arms request was significantly stripped down at the insistence of pro-Israel senators, the package still included F-15 fighter aircraft desired by the Saudis and insisted on by Reagan.

No resolution of disapproval against the Saudi sale was introduced by such pro-Israel senators as Alan Cranston, Bob Packwood and Rudy Boschwitz. More surprisingly, Sen. Howard Metzenbaum, a battler for Israel, publicly supported the sale and thereby preempted any floor move to block it. Metzenbaum's acquiescence disheartened the American-Israel Public Affairs Committee, which normally calls all Mideast signals for Israel's supporters in Congress and wanted no F-15 sale.

Despite the lopsided vote approving the Smith-Levine amendment blocking Stinger sales except to NATO countries and ''major non-NATO allies'' (which include Israel), it will not hold up their sale to Bahrain. Chances are slim that the House-imposed ban will get through the Senate, although a Senate subcommittee did pass a ban yesterday. Even if it did pass the Senate, President Reagan would be certain to veto it.

Floor debate in the House told why. ''We have serious problems here because of congressional micromanagement,'' Republican Rep. Gerald B. Solomon of New York told the House. ''This amendment is driving the administration or any future administration to deal covertly with these countries, as opposed to overtly.''

The Reagan administration has not been so articulate in expressing its own concern about carrying out American policy abroad. Having lost so much for so long to congressional demands for micromanagement of intimate White House business, the president in his waning months is standing firm on one small sale to one small country and hoping it becomes a precedent against power-hungry legislators.