A State Department rule requiring American diplomats in Moscow to get advance approval from the U.S. ambassador for any meetings they may have with ordinary Soviet citizens has seriously restricted such contacts, according to U.S. sources here.

As a result, according to the sources familiar with the effect of the new procedure, the quality and volume of information based on contacts with Soviet citizens has declined.

Moreover, the ruling clearly marks a shift in the Carter administration's policy toward dissent in the Soviet Union. After starting with open support for political dissidents that even included a personal letter from the President to one of their leaders, the administration has decided to cut down the number of contacts with dissident Soviets in favor of quiet diplomacy similar to that pursued by former Secretary of State Henry Kissinger.

State Department officials yesterday denied that the number of contacts of U.S. personnel in Moscow had fallen off or that the embassy's reporting had been affected adversely.

Officials described the move, which went into effect last summer, as "a matter of operating procedure" that permits Ambassador Malcolm Toon to keep "close tabs" on his staff.

Under the new rule, all staff members of the U.S. embassy in Moscow and their spouses are required to give 24-hour notice of intentions to meet Soviet citizens. Only a few of the 130-odd personnel have been authorized to meet with political dissidents or Jewish activists, according to the sources.

State Department officials said the objective of the new "operating procedure" was to cut down on the volume of contacts while at the same time have "those officers who have outside contacts know all the facts involved."

Officials admitted privately that in the past few years, U.S. contacts with Jewish and dissident groups had proliferated beyond manageable proportions, creating numerous opportunitues for upsurges of strain in U.S. Soviet relations.

They also pointed to the delicate nature of the U.S.-Soviet relationship, apparently a reference to the ongoing arms limitation talks between Moscow and Washington as well as a Soviet campaign of threats, arrests and exile against political dissidents and Jewish activitists.

Before President Nixon's 1972, Moscow cow visit and the advent of Soviet-American detente, American diplomats and journalists in Moscow were scrambling for an occasional contact with ordinary Russians.

Until then, the Americans were almost completely isolated from Soviet life and their contacts were restricted to a handful of Soviet government officials authorized to deal with foreigners.

The upsurge of dissent and the Jewish emigration movement in the early 1970s widened the range of U.S. contacts. But U.S. diplomats in Moscow never came close to having the kind of contacts that Soviet diplomats enjoy in Washington.

One former U.S. ambassador suggested yesterday that the Carter administration's current objective may be to expand contacts of U.S. diplomats with members of the Soviet establishment. To do that, this former official said, the administration may have been willing to trade off the volume of contacts Americans enjoyed with Soviet citizens outside the establishment.

State Department officials rejected this line of thinking and maintained that the policy remained one of encouraging "broad contacts" with all sectors of Soviet society.

The Moscow situation contacts with that in Latin America, where some U.S. diplomats have recently assumed the role of human rights watchdogs. Steps taken by the diplomats range from visits to imprisoned dissident intellectuals in Uruguay to the highly visible official presence by the American ambassador at a human right-oriented function in Chile.