Senate Judiciary Committee action on Clarence Pendleton, President Reagan's nominee as chairman of the U.S. Civil Rights Commission, has been delayed while the FBI conducts a new background investigation at the request of the White House.

Sources in San Diego, where Pendleton is president of the local chapter of the Urban League, said FBI agents are asking about Pendleton's handling of a $94,000 league grant from the Department of Health and Human Services in 1980 for family planning assistance.

Pendleton, 51, a conservative Republican and maverick in the Urban League, is a political protege of White House counselor Edwin Meese III. He was nominated last November to replace Civil Rights Commission chairman Arthur S. Flemming, who was fired after publicly criticizing the Reagan administration's civil rights policies.

The Judiciary Committee heard testimony from Pendleton last Friday and had scheduled a vote on Tuesday. It was postponed when the committee was notified of the reopened investigation.

It was the third time in less than a month that the administration's nomination of a black to a civil rights position has run into trouble.

The White House withdrew the nomination of William M. Bell to head the Equal Employment Opportunity Commission in mid-February after civil rights groups and senators protested that he was not qualified.

And, last Friday, B. Sam Hart, a Philadelphia radio evangelist and favorite of the Christian New Right, withdrew from his nomination to the Civil Rights Commission. This followed disclosures that he was deeply in arrears on several Small Business Administration loans and outcries over his remarks opposing the Equal Rights Amendment and civil rights for homosexuals.

The Pendleton grant inquiry, according to Victor Vilaplana, chairman of the San Diego Urban League's finance and budget committee, began last October at the request of Pendleton, who was concerned that many stored records relating to the grant were destroyed by rain coming through a leaky roof.

"Nothing has come to our attention to suggest that the funds were misused or misspent," Vilaplana said yesterday. "The only thing we're looking into is the accounting treatment. The funds are now in our financial statement as a 'restricted liability.' We want to understand what that means and whether that is appropriate."

Vilaplana confirmed that the San Diego league's board has also taken action in recent months to tighten up the management of the league. It became concerned after learning that under Pendleton the league was late in making payments to Social Security and the employe pension fund and in its quarterly payments of employe withholding taxes.