Soviet Ambassador Anatoliy F. Dobrynin has told the Carter administration that the Kremlin is bound to resent American support of dissident Andrei D. Sakharov as an unwarranted intrusion into Soviet domestic affairs.

Dobrynin registered his complaint in a telephone call to Secretary of State Cyrus R. Vance shortly after the State Department on Thursday spoke out in behalf of the nuclear physicist, who is Russia's leading dissident. The department coutioned against attempts "to intimidate" or silence Sakharov.

The exchange is the first sign of irritation between the Carter administration and the Soviet Union.

Dobrynin, in effect appeared to be cautioning the Carter administration that taking up the dissidents' cause may jeopardize prospects for expanded U.S.-Soviet relations. Vance is planning to visit the Soviet Union around the end of March to launch new negotiations on the stalled nuclear Strategic Arms Limitation Talks. (SALT).

The State Department, through a spokesman, acknowledged that Dobrynin had telephoned Vance, but declined to say whether Dobrynin had made "a complaint or a protest." There was no comment from the Soviet embassy. Before and since President Carter's inauguration, the Soviet Union has hailed the outlook as auspicious for improved U.S.-Soviet relations.

Appeals on behalf of Sakharov intensified yesterday. A personal appeal to President Carter from Sakharov was delivered to the State Department by a New York attorney, Martin Garbus, who returned from Moscow this week.

In the letter, dated Jan. 21, the day after the President's inauguration, Sakharov asked the President to act quickly "to defend those who suffer because of their non-violent struggle for justice."

Sakharov said, "Here we have an almost unbelievable situation. Not only in the U.S.S.R., but in all the countries of Eastern Europe."

He urged President Carter to move quickly especially to secure the release of 15 political prisioners in the Soviet Union named in the letter, and speak out for the rights of all who seek fundamental human rights.

Another appeal, sent by four dissident Soviet writers to world leaders, said that Sakharov, 1975 NOBEL Peace Prize winner, is especially exposed for speaking out.

"For him personally it is a mortal dange," said the appeal, addressed to President Carter, Pope Paul VI, and European leaders. That statement was distributed to Western reporters' by Lidia Chukovzkaya, Vladimir Vionovich, Lev Kopelev and Vladimir Kornilov.

The letter and supporting documents handed over at the State Department by Garbus were presented to Philip C. Habib, under secretary for political affairs, and other officials.

Garbus said he went to the Soviet Union as a tourist, and ended up in Sakharov's apartment, where the Soviet scientist wrote his impassioned appeal to Carter. A State Department spokesman said "the letter will be transmitted to the president." Garbus said Vance "has shown great courage and dignity" in dealing with Sakharov's appeal.

The State Department announced yesterday that Vance has appointed Marshall D. Shulman, a prominent specilist on Soviet Affairs, including nuclear arms controls, as his special consultant on Soviet affairs.

Shulman, 60, is director of the Russian Institute at Columbia University, and served as a special assistant to Secretary of State Dean Acheson in 1950-53.