Senate Majority Leader Robert C. Byrd (D-W.Va.) said yesterday that the Senate will permit radio broadcasting of one of its debates for the first time when it takes up the Panama Canal treaties later this year.

Byrd said he found "unanimous support for audio transmission of the debate" in a survey of the Senate Rules Committee, which would have to approve the broadcast. "Audio transmission is virtually assured," he said.

The canal treaty debates will, however, not be televised, Bryd said at his regular Saturday morning news conference. He said television presents "technical problems" such as distractingly bright lighting and obstrusive cameras that would interfere with a Senate debate.

Byrd said he is "cautiously optimistic" that the Senate will muster the two-thirds majority needed to approve the treaties. He indicated that the Senate Foreign Relations Committee's adoption Friday of a new article guaranteeing U.S. rights to defend the canal and to send warships through without waiting in an emergency will ease Senate approval of the treaties.

"I detect a shift in opinion in the Senate already," Bryd said. "I think the shift was given impetus by events of recent days, and I think that shift will continue. I think the president's address to the nation will contribute to that shift, because it will provide more public understanding" that the treaties are in the best interests of the United States.

President Carter has scheduled an address to the nation Wednesday to discuss the treaties.

In 1974, the Senate Rules Committee voted to allow live radio and television broadcasting of the expected impeachment trial of then-president Nixon, but the trial never took place because of Nixon's resignation.

Byrd said that as far as he knows the Senate has never allowed live broadcasts of a floor debate.

On other matters, Byrd said the controversial firing of David W. Marston, the politically appointed Republican U.S. attorney in Philadelphia, does not suggest to him that the system of political appointments of prosecutors and judges should be changed.

"The po lical system has worked very well in the past," said Byrd, a past master of the political process. "It focuses responsibility of the selection of U.S. attorneys and judges on the party in power. If they're bad, the responsibility falls on the party in office . . .

"This is how Mr. Marston was appointed, and if he did a good - as apparently he did - it seems to be a good reflection on the system under which he was pointed.