The District of Columbia's efforts to obtain title to the Robert F. Kennedy Stadium, tied to its campaign to bring baseball back to Washington, got a boost yesterday with the announcement that the Senate will start moving on the issue this month.

Sen. John W. Warner (R-Va.), who is taking the lead on the measure in the Senate, said yesterday he would chair a hearing on Oct. 10 and hoped to see final congressional passage of a bill before the end of this year to transfer ownership of the stadium to the District.

"I'm optimistic that we can move it," Warner said. "If we are going to give the city officials who want the baseball franchise some help, we should do this."

The ownership legislation had been passed by the House with no difficulty, and the problem in past years has been in getting the Senate to take action.

City officials welcomed Warner's announcement and said passage of the legislation would help their efforts to get a baseball team.

"We would like to get it the bill out before the end of this session because we are trying to get ready for baseball in 1987," said City Council member Frank Smith Jr. (D-Ward 1), chairman of the D.C. Baseball Commission. "The senator Warner has taken a keen personal interest in this, and he will keep it on track."

The city wants to take ownership of the stadium in Northeast Washington to renovate it for a hoped-for baseball team.

The House on June 24 approved legislation to transfer stadium ownership from the federal government to the District. The Interior Department, which now has jurisdiction over the stadium, and the U.S. Office of Management and Budget have both agreed to the transfer, congressional aides said. The House approved the measure by voice vote without debate or expressed opposition.

The House had passed stadium transfer legislation in 1983, but the bill died in the Senate at the end of the 1984 congressional session. It had languished in the Senate Governmental Affairs subcommittee on the District, chaired by Sen. Charles McC. Mathias Jr. (R-Md.), which took no action on the measure and held no hearings on it.

This year the bill was referred to the Senate Energy and Natural Resources Committee, of which Warner is a member. City officials had been concerned that the change in jurisdiction might hamper their efforts to obtain passage, because that committee was not familiar with the issue.

"The whole problem on the Senate side was building enthusiasm for why these very busy senators should be dealing with RFK Stadium in the District of Columbia," said Julius Hobson Jr., legislative director to D.C. Del. Walter E. Fauntroy. "It will pass now," he predicted.

Smith said he believes that Washington is at the top of the list of at least a dozen cities vying for a baseball franchise, and he hopes that major league baseball owners will approve a team for Washington at a meeting in December.

The City Council last week approved a $13.7 million general obligation bond issue to finance a major renovation of the stadium if the city gets a team.

Warner said he thinks the sentiment in the Senate for a ball team here is building. "I'm using the ploy that we should call them the Senators and give ourselves a little boost."