Former Health, Education and Welfare secretary Joseph A. Califano Jr. said yesterday he will serve as special counsel to head the House ethics committee's investigation of alleged sexual misconduct and drug use involving members of Congress.

In a Capitol press conference, Califano said the committee and House leaders "assured me that I will have the independence, the authority, and the resources to carry out whatever investigation is needed to probe fully the allegations that have been made."

The investigation will examine allegations by former pages and by Rep. Robert K. Dornan (D-Calif.), who says that a D.C. policeman who posed as a Dornan aide to investigate a drug ring told him about drug use by members of Congress.

Califano said he has been asked to complete the investigation "as expeditiously as possible," but that no time limit has been set.

The Justice Department is conducting separate investigations to determine whether criminal charges should be brought. The ethics committee investigation could lead to recommendations for internal disciplinary measures such as censure or expulsion.

Califano, 51, a partner in the law firm of Califano, Ross and Heineman here, served as secretary of Health, Education and Welfare from 1977 to 1979. He said the committtee would pay his firm $100 an hour for partners and $75 an hour for associates, adding that the sums are "far below" his regular rates.