To the chagrin of Turkey's allies. Prime Minister Bullent Ecevit has been flirting politically with Soviet President Leonid Brezhnev. Ecevit, unable to coax the United States out of the arms of the Greeks, is playing the role of the rejected suitor. He will call at the Kremlin this week to exchange toasts and sign a "good neighbor" pact with Brezhnev.

"We are worried about the Ecevit Brezhnev meeting and any agreement they may reach," conceded a top NATO strategist. Because of the U.S. arms embargo, the officer continued, "the state of the Turkish armed forces is deplorable." Unless the ban is lifted, NATO leaders believe, the Turks will ease out of the Western camp and may begin to purchase Soviet weapons.

From the military viewpoint, this would be disastrous. Turkey is the bulwark that protects NATO's southeastern flank. The Turks share a 270-mile border with the Soviet Union and control the strategic straits through which Russia's Black Sea fleet must pass. Ankara devotes nearly a quarter of its revenues to its 500,000-man military force - among the allies, second only to the U.S. force in size.

The NATO high command, therefore, fears the departure of Turkey would imperil the security of the West. This is an attitude that the Turks are eager to encourage. Ecevit has threatened to forge a "new national-security concept" and diversify his sources of weaponry in order to lessen Turkey's dependence "on the decision or indecision of other countries."

His new foreign policy, Ecevit has said, "will try to promote mutual trust with the countries in this area." Furthermore, he added, Turkey will attempt to avoid any NATO commitment that might arouse the "concern and mistrust of other regional countries." Put another way: Turkey will strive to be more neighborly toward the Soviets.

Taken at face value, this would be a shocking turnabout. For years, the Turks were as hostile toward Moscow as they were faithful to NATO. But after their weapons were cut off, they began casting come-hither glances across the border. Soviet Prime Minister Alexei Kosygin responded in December 1975 by venturing into Turkey. He left with a pledge that the two nations would sign a "political document on friendly relations and cooperation." This is the instrument that Ecevit will now endorse in Moscow.

There need be no fear, the Turks assured their NATO partners, that Turkey was preparing to bolt the alliance. It was simply a matter, they said, of developing "political and economic relations" with their communist neighbor.

But we have had access to Ecevit's secret correspondence with Brezhnev, which contains some fawning language. In the name of detente, the Turkish leader has offered to set aside old antagonisms and to promote friendship, disarmament and peace.

"Mr. President, since the relentless arms race in all parts of the globe is not in line with the detente process," Ecevit wrote to Brezhnev last March, "Turkey is resolved to strongly support disarmament efforts . . . and to contribute to the elimination of causes underlying the arms race."

The letter concluded: "I would also like to repeat the importance which Turkey attaches to maintaining and developing relations of friendly cooperation with the Soviet Union based on mutual respect and to express my conviction that the further development of good-neighborly relations between our two countries will be a valuable contribution to peace."

But if a balmy new breeze is blowing between Ankara and Moscow, it is not expected to thaw all the ice. For the Turks and the Russians are traditional enemies who have fought a dozen wars. Turkey's conservative military leaders simply would never accept a Soviet-Turkish military accommodation. Turkey is also an Islamic country and therefore - in the opinion of one U.S. analyst - "immune to communism."

Nor is the State Department greatly alarmed over a Soviet-Turkish rapprochement. "Other European countries have dealings with Moscow all the time," said one official. "Why not Turkey?" Ecevit himself made this point in a recent closed-door session with congressional leaders. He was asked to explain the motive behind his trip to Moscow. No one, snapped Ecevit indignantly, asks that question of Cyrus Vance when he visits Russia.

Even the Pentagon is unperturbed by the Turkish-Russian sweet-talk - so unperturbed, in fact, that it has briefed the Turks on the sensitive and sophisticated Airborne Warning and Control System (AWACS). A cablegram, labeled "Limited Official Use," from U.S. Ambassador to Turkey Ronald Spiers reveals that Turkish leaders were briefed on the AWACS March 3.

In relaxed moments, the Turks themselves admit that the current infatuation with the Soviet Union will never blossom into a real love affair. The Russians "build a lot of showcase projects and then try to extract political favors," a high-level foreign ministry official told my associate Joe Spear in Ankara. The Soviets, continued the official, "would like to 'Finlandize' Turkey" - turn it into a neutral country on good terms with Moscow. But the Turks, he said with a wily smile, quietly resist these efforts."