While most of the country was cutting into Thanksgiving dinner, Alexander Kostomarov poured himself a cup of tea chased with medication to keep his body from eating its vital proteins.

Kostomarov, a Russian immigrant, today entered the 22nd day of a hunger strike that he hopes will persuade Soviet authorities to let the wife and son he left five years ago join him here. He says he will not continue his hunger strike to the death.

It is a campaign with dubious prospects, according to the State Department, which pointed to the poor Soviet track record in bending to public pressure from immigrants to the United States.

But for Kostomarov, an electronics engineer, his own body was the most he could give to his cause. "In this particular case a hunger strike is one of the very few ways to act. I don't know any other way," he said.

Kostomarov left the Soviet Union in 1979 intending to bring his wife, Tatiana, and son, Sergey, 18, to the United States shortly afterward. Both stayed behind to care for her ill mother, but are eager to leave now, he said. Both now suffer from medical problems but cannot get sufficient care, he said. Despite repeated appeals to the Soviet authorities, there is no indication the family will be allowed to leave.

Kostomarov's family is one of 100 on the State Department's "divided families" list, which is presented at high-level meetings between the two countries. The list was last presented by Secretary of State George Shultz at a meeting with Soviet Foreign Minister Andrei Gromyko in September. The Soviets typically have little or no response to the list.

Kostomarov's case is complicated by the fact that he was forced to divorce his wife in order to get permission to emigrate. The divorce now makes it easier for the Soviets to ignore their obligations under the 1975 Helsinki Accords, in which they pledged to give special consideration to uniting families living in different countries.

A diplomat at the press office at the Soviet embassy said of the case: "I don't think it would be appropriate for us to comment on the case, for us to appear in a story about a defector. . . . A defector means a defector."

Kostomarov is in stable condition, according to his physician, and has said he will not starve himself to death. "It seems like a contradiction, but I'm not going to stop and I'm not going to die," said Kostomarov. "We found the answer; we have a committee" of supporters to continue the campaign, he said.

A local Quaker group and friends from New York, Baltimore, the District of Columbia and Paris have pledged to start a rotating fast among themselves, a tactic now widely used among dissidents in the Soviet Union.