John M. Poindexter, the all-but-invisible admiral who became President Reagan's national security affairs adviser last month, is being tested early and often in his new job. So far, the results do not seem promising.

First came the issue of what to do about terrorism supposedly sponsored by Libya, on which administration officials talked like tigers and responded like tabby cats with economic sanctions in which most of our allies have refused to join. Now, it is the less dramatic but more consequential challenge of the latest Soviet nuclear arms-control proposal, which caught the Reagan administration thoroughly off-guard.

Poindexter can be excused for the confusing comments made by other officials about Libya after the terror bombings at the Rome and Vienna airports. He was new to the job and off-duty when various administration factions offered their conflicting remedies.

But Poindexter is the point man in coordinating administration arms-control policy, and he has moved with less than deliberate speed in fashioning a U.S. response to Soviet leader Mikhail Gorbachev's proposal for a staged reduction of nuclear weapons. It calls for elimination of the superpower nuclear arsenals by the end of the century.

In its utopian character and public relations appeal, the Kremlin offer seems a sophisticated version of Reagan's grandiose first-term proposals for doing away with the nuclear arsenals that give the United States and the Soviet Union the power to blow each other to kingdom come. Yet the administration seems paralyzed by the echo from Moscow. Reagan's response has been to say that "we're very grateful" for the proposal, while his subordinates were anonymously denouncing it as a propaganda ploy.

Behind the scenes, at the arms-control planning group charged with cooking up a response, chaos prevailed for days before it was decided to send a letter to the Soviets exploring the possibility of an agreement limiting medium-range missiles in Europe. Everyone involved agrees that the Soviet plan has many defects, but State Department experts consider some aspects of it forward-looking. Defense Department specialists believe that the proposal goes backward. As usual, the president is detached from the process while focusing on the bromides of the State of the Union address he is to deliver Tuesday.

Whatever its merits, the Soviet proposal has succeeded in once more revealing the deep divisions within the administration on arms control. Pogo's observation that "we have met the enemy and he is us" applies. Conservatives would argue, and the Afghans would attest, that the Soviets are the real enemy, but this hardly excuses the administration's failure to produce a timely response that advances the arms-control dialogue.

Poindexter is an honest broker with access to the president, but he has yet to grasp the special responsibilities that go with this position. For one thing, Poindexter holds the only position of authority from which a unified response can be hammered out. The chief contribution of his predecessor, Robert C. McFarlane, was that McFarlane recognized that the national security affairs adviser must take the lead role in arms control. The relative success of the Geneva summit is chiefly a testament to McFarlane's persistence in knocking heads and achieving compromises.

McFarlane, Secretary of State George P. Shultz and the practical arguments of Reagan's political advisers persuaded the president to engage the Soviets in an arms-control dialogue. McFarlane, with help from the Joint Chiefs of Staff, then convinced Reagan that a new missile-defense proposal would enable him to seize the diplomatic offensive at a time when the U.S-Soviet dialogue consisted largely of name-calling.

Reagan oversold himself on the Strategic Defense Initiative (SDI), but it accomplished its political purpose. Now, someone needs to persuade Reagan that he can make concessions on the SDI in the interests of winning real reductions in offensive nuclear weapons.

If Poindexter holds any such bold and heretical thoughts, they are well concealed. His intellectual ability, demonstrated by his academic record at the Naval Academy and Cal Tech, was widely heralded when he took over in December. But he has shown no signs of demonstrating the political leadership needed to break the administration gridlock on arms control.