The United States has signed an agreement with Turkey to build one new air base and modernize two others in eastern Turkey to put NATO fighter-bombers within easy striking distance of Soviet forces nearest to the Persian Gulf.

Under the agreement initialed last month by Richard N. Perle, U.S. assistant secretary of defense for international security policy, and Gen. Necdet Oztorun, deputy chief of staff for the Turkish military, the United States and its NATO partners will spend millions of dollars to modernize airfields at Erzurum and Batman and to build a third base at Mus.

Perle said the bases would strengthen NATO's southern flank, which is now confronted by 17 Soviet divisions.

A Turkish official said the Soviets also have about 150 airfields that pose a threat to Turkey.

Pentagon officials said they hope the bases also will give the Soviets second thoughts about moving troops southward into oil-rich Iran from the mountainous southwestern Transcaucasian region between the Black and Caspian seas.

Pentagon and Turkish officials said the Soviets have recently strengthened forces and constructed airfields in the region.

Asked about the new NATO aerial strength that would be made possible by the agreement, a high-ranking Turkish embassy official here, who did not want to be quoted by name, said, "The Soviets won't like it, but it's peanuts compared to what they've got facing us."

NATO fighter-bombers flying out of the base to be built at Mus could cover the entire Transcaucasian border region without having to refuel in midair. Mus also will put NATO planes 550 miles from Tehran and 700 miles from Iran's oil refinery center at Abadan at the head of the Persian Gulf.

By contrast, the Rapid Deployment Force base the United States hopes to build on the Red Sea at Ras Banas, Egypt, is 1,000 miles from Abadan. The U.S. supply base on the island of Diego Garcia is 3,000 miles from Abadan.

The Reagan administration sought Turkey's permission to use the three air bases for the Rapid Deployment Force, as well, in an emergency but Ankara has refused to go along with this part of the proposal, sources said.

Although Pentagon officials said the three bases in eastern Turkey will be used mainly for NATO fighter-bombers, the runways likely will be built long and wide enough to handle long-range bombers, huge cargo planes like the Air Force C5 and tanker aircraft.

"You can't pick a better place than Turkey for defending the Persian Gulf," said one congressional staff aide involved in annual Capitol Hill controversies over military assistance to Turkey.

Pentagon officials said they will have to fight for Turkish aid on two fronts before Congress next year, one for the bases and the other for more money to rearm Turkey.

They said the Reagan administration will ask Congress next year for "a significant increase" above the $465 million requested for weapons for Turkey in fiscal 1983, and Congress has not yet approved that amount.

The administration has been steadily increasing the account financing weapons for Turkey, from $250 million in fiscal 1981 to $400 million in fiscal 1982, on grounds that NATO's southern flank needs strengthening. One source of congressional opposition to Turkish aid has been the continued presence of Turkish troops on Cyprus, fueling the longstanding dispute between Greece and Turkey on that issue.

Opponents also are expected to protest that increased military aid, both the bases and arms, would further strengthen the hand of the military regime now running Turkey.

Turks will go to the polls today to vote on a new constitution that would extend military rule for seven years and forbid most former civilian party leaders from engaging in politics for 10 years.

If the constitution is approved, Gen. Kenan Evren, head of state and chairman of Turkey's ruling five-man National Security Council, would be president for seven years. Evren and fellow generals seized power in September, 1980, from an elected conservative government which was buffeted by political turbulence and labor unrest.

One clause in the constitution would prevent former premiers Suleyman Demirel and Bulent Ecevit from forming new parties or running for public office for the next 10 years.

The constitution also would empower leaders to curtail citizen rights and press freedoms under some conditions. The executive would also have more power than Turkey's legislative or judicial branches.

One critic of the constitution, Atilla Sav, president of the Union of Turkish Bar Associations and a former labor minister, has said, "The essence of fundamental rights and freedoms in Turkey are being taken away with the new constitution."

Evren, in urging citizens to vote "yes," has stressed that the new constitution is the key to stability for Turkey.