By a vote of 234 to 168, the House gave final congressional approval yesterday to President Carter's request for $13.3 million to register 19- and 20-year-old young men for a possible military draft.

As soon as Carter signs it into law, the American Civil Liberties Union has said it will file suit in federal court challenging the constitutionality of the legislation because it does not also require registration of young women. The president has authority to order registration of young men, but Congress refused to authorize him to register women also.

The administration's plan, unless blocked by the courts, is to conduct registration during a two-week period -- one for each age group -- later this summer. The 4 million young men affected would go to their local post offices and fill out cards giving name, age and address which would be kept by the Selective Service system.

Carter asked for the funds nearly six months ago, after the Soviet invasion of Afghanistan, to show American resolve. The administration says registration now, even though there would be no classification or training of the young men, would provide a significant head start on mobilization in an emergency. The proposal has had hard going because many members viewed it as a meaningless gesture, without training, but one which would provoke strong opposition by young people and could result in sending many of them to prison for refusing to register.

During yesterday's final debate, Rep. Ronald E. Paul (R-Tex.) noted that many members supporting the registration of young men have strongly opposed the registration of guns, though the purpose is the same -- to find out how many are out there and where. "They think less of their kids than their guns," he said.