Three members of the City Council yesterday added their support to a draft-Kennedy movement in the District of Columbia. The move has grown to include nearly half the members of the D.C. State Democratic Committee.

Council members Betty Ann Kane, John Ray and Nadine Winter announced their affiliation with the D.C. Committee for a Democratic Alternative at a press conference at the District Building at which they cited varying reasons for forsaking incumbent President Carter in favor of Sen. Edward M. Kennedy (D-Mass.).

The committee has invited all elected Democratic officials in the city to join its ranks. But Mayor Marion S. Barry, Council Chairman Arrington Dixon and D.C. Del. Walter E. Fauntroy, the top elected Democrats, all have declined to join the draft-Kennedy movement, at least for the time being.

D.C. Democratic Chairman Bob Washington remains a Carter loyalist, while some other Democrats reportedly are reluctant to turn their back on the president for fear the White House would punish dissenters by withdrawing or withholding support for vital city projects.

It was dissatisfaction with the Carter White House, as it affects D.C. matters, that Kane, Ray and Winter cited yesterday as reasons for turning to a Kennedy candidacy.

"I'm interested in social problems," said Winter, the Ward 6 member and Council chairman pro-tem, "and Senator Kennedy can best address these problems and pull the nation together."

Ray, an at-large councilman, said "Teddy Kennedy gives the country an opportunity to fill the leadership void that has existed in the office of the president . . . except for a brief period in the 60s . . . since 1953."

Kane, the other at-large member, said, "on many matters of importance to the city, President Carter has been a disappointment."

The District of Columbia's draft-Kennedy committee is one of 48 similar organizations, in 45 states, including Maryland and Virginia, Puerto Rico and Paris, France, according to the National Clearing House to Draft Kennedy.

Joseph L. Rauh Jr., a member of the D.C. group, and vice president of Americans for Democratic Action, said the local committee "is only of importance as a means of helping others. Jimmy Carter couldn't beat Ted Kennedy in the District if he had George Washington as his campaign manager and Abraham Lincoln as his speechwriter."