A South Carolina federal trial judge has emerged as the leading candidate to replace Robert H. Bork, who resigned this month as a federal appeals court judge here, administration officials said yesterday.

The sources said that at a White House meeting yesterday, the Justice Department recommended U.S. District Judge Karen Henderson of Columbia to fill the vacancy on the influential D.C. Circuit Court.

It could not be determined whether a final decision to nominate Henderson was made at the meeting.

Henderson, 43, was nominated by President Reagan in 1986 to become the first woman federal judge in South Carolina.

She is a former deputy attorney general of South Carolina who specialized in constitutional law, local government law, administrative law and public finance in private practice before being named to the bench.

If nominated, Henderson is expected to receive support from South Carolina Sen. Strom Thurmond, the ranking Republican on the Senate Judiciary Committee, who recommended Henderson for the district court position.

However, officials of the District of Columbia bar have complained repeatedly about the lack of local lawyers on the appeals court, an issue that has drawn the sympathy of some Judiciary Committee members, including Sen. Edward M. Kennedy (D-Mass.).

Kennedy and other Judiciary Committee members also have pressed the administration to nominate more minority-group members and women to federal courts, both here and around the country, and Justice Department officials said they were searching for a woman to replace Bork.

Others considered for the seat include Kimba Wood, a New York lawyer whose nomination to a federal trial court there is now before the Judiciary Committee; Pamela Rymer, a federal trial judge in Los Angeles, and District lawyers Judith Richards Hope and Carla Hills.

Bork announced his resignation Jan. 14, three months after the Senate defeated his nomination to the Supreme Court.

His departure leaves the 12-member court, often described as second in importance to the Supreme Court, divided roughly six to five between conservatives and liberals, making it a priority for the Reagan administration to fill the vacancy.

Henderson, a 1969 graduate of the University of North Carolina law school, was rated "well-qualified" by the American Bar Association, with a minority rating her "qualified" when she was nominated to the district court in 1986.

Answering a Senate Judiciary Committee questionnaire at the time, she emphasized the importance of judicial restraint.

"If the judicial branch usurps the legislative and executive branches it will eventually end in tyranny," she said.