President Reagan lashed out yesterday at racial "quotas" to correct civil rights abuses, and called for the Senate to confirm his promotion of William Bradford Reynolds to associate attorney general.

Reagan, in his weekly radio broadcast, said he has always opposed quotas in civil rights cases because they are discriminatory and simply create a new form of bias. He said quotas should be abolished to "return civil rights laws to their original meaning."

The president termed Reynolds, now head of the Civil Rights Division and often criticized by civil rights groups, a "tireless fighter against discrimination" and said he is opposed "by some who favor the discrimination of quotas." But, he said, "I'm confident the Senate will confirm him."

Civil rights leaders deny that numerical goals and timetables for increases in minority employment or school enrollment constitute quotas. They say that some of the administration's policies would dismantle carefully conceived procedures to reverse the effects of discrimination. They say the administration would undo court-ordered school desegregation, weaken antidiscrimination laws in education, and strip away the power of courts and agencies to require special goals for hiring minority workers..

Democrats, in their response to the president, discussed a different subject. Rep. David E. Bonior (D-Mich.) called on Reagan to join with Democrats in a campaign to cut waste in military spending.

Bonior said Defense Department outlays are "out of control" and "the Pentagon simply cannot spend all the money it has been given. Today there is $51 billion sitting in the Pentagon left over from past years."

In spite of this, "Mr. President, . . . too often it seems you have asked us to increase military spending without telling us where the money will be spent," he said.