Carter administration sources confirmed yesterday that Eleanor Holmes Norton, New York City's human rights commissioner, is President Carter's choice to head the embattled Equal Employment Opportunities Commission.

The commission may be expanded and given enforcement powers for thefirst time in its 12-year history, it also was learned yesterday.

Norton, a 39-year-old black lawyer, has been strongly supported by women's and some civil rights groups. "The President will nominate her unless problems turn up in her background check," one source said.

The EEOC has been widely criticized in recent years, both for trying to reduce the backlog by eliminating files for people who can no longer be found. It has had two chairmen and an acting chairman in two years.

A General Accounting Office report said late last year that before 1972 the agency had made only limited progress in eliminating discrimination.

Carter said before his inauguration that he wanted to consolidate some or all of the seven federal agencies that have some jurisdiction over equal employment opportunity.

Mark Siegel, Carter's deputy assistant for policy analysis, told a reporters' meeting yesterday the White House was considering expanding EEOC to include some of the functions of the six other EEO agencies, and giving it enforcement powers for the first time.

Siegel did not spell out any details: The EEOC has never been able to order employers to change their policies when it finds discrimination.

From its creation in 1965 until 1972, it could only ask the Justice Department to take offending employers to court if its own attempts at conciliation failed. In 1972 Congress gave the EEOC the right to sue employers in U.S. District Court. Current agency policy is to go to court only if conciliation fails.

The National Women's Political Caucus, which strongly supported Norton for the job, issued a statement saying " . . . The President in this case sought out and found the most qualified person in the country for this job . . . we're elated."

Organized labor and some civil rights groups had been backing Ronald Brown, director of the Washington Urban League, for the job.