The Cuyahoga County Democratic Party Central Committee, its ranks thinned to about 20 percent of normal by a boycott and holiday weekend absentees, today approved a resolution to draft Sen. Edward M. Kennedy (D-Mass.) for president.

The measure, which simply urges Kennedy to run in 1980, carried by a smaller-than-expected margin in a standing vote of the fewer than 300 precinct workers who attended the party convention at the Cleveland Plaza Hotel. The county has 1,553 central committee members.

The action nevertheless put the Cuyahoga County party, the largest in the state, on record as the first major political organization in the United States to approve a Kennedy draft formally.

Party Chairman Timothy Hagan, who helped initiate the Kennedy campaign here and then disavowed it Friday, returned to his original position at today's meeting, saying he could not dissuade other Kennedy loyalists from offering the resolution to the committee.

He said the vote, which he estimated to be "60 to 40" to "65 to 35", was "closer than I thought iw would be . . . It was an expression of Democrats meeting in a body. But I wouldn't call it an overwhelming mandate."

It was understood that a number of Democratic officeholders here boycotted the convention because they didn't favor the resolution.

Hagan had met Friday with former governor Michael V. DiSalle, a Washington lawyer, in the latter's office. DiSalle had urged Hagan to drop the draft plan because Kennedy has repeatedly said he is not a candidate.

Hagan told reporters after that meeting that he would return here to argue against the resolution. However, the chairman said he was unable to persuade other pro-Kennedy Democrats here to kill or postpone the action.

After the vote, DiSalle said in Washington that Hagan had called him Friday night to say that he could not block the vote. DiSalle addded, "They're got banned and stuff. But they don't have a candidate."

Several of those who spoke for the resolution criticized President Carter for reneging on campaign promises on social issues. Cleveland City Council-woman Artha Woods said of Carter, "There is no place in American politics today for a man of forgotten promises, a man of forgotten dreams. You have failed to cast us blacks even a handful of your peanuts."

Others blamed the president for failing to halt inflation, particularly in fuel and food costs. "I don't hear the leader saying it must stop," said Michael Climaco, a party vice chairman.

But Martin Hughes, international vice president of the Communications Workers of America, defended the president, citing improved employment figures under the Carter administration.

He also said a Democratic split in the presidential race would turn over the White House to John Connally or Ronald Reagan "on a silver platter."

Hughes said after the meeting that the turnout was so light and the vote so close that it was "rather meaningless, don't you think?" But Hagan said he hoped the action would at least send Carter a message that "there's a widespread disagreement with his policies and programs."