Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) said yesterday he will order an investigation into charges that a committee staff lawyer attempted to intimidate a black law professor against testifying in favor of the Supreme Court nomination of Judge Robert H. Bork.

"I don't think there is much to this, but as in all such matters where a request for an inquiry has been made, we will respond to the request," Biden said.

The request for an investigation was made by Sen. Gordon J. Humphrey (R-N.H.), a conservative Judiciary Committee member and one of Bork's strongest supporters.

The incident involved a Sept. 27 conversation between Linda Greene, a committee staff lawyer for Sen. Howard M. Metzenbaum (D-Ohio), and John T. Baker, an Indiana University Law School professor. Greene has said she called Baker as a friend to warn him that his scheduled appearance at the Bork confirmation hearings Sept. 28 might turn into a painful ordeal.

Baker told Metzenbaum in a letter last week that he took "complete responsibility" for his decision not to testify.

In a telephone interview yesterday, Baker said that Greene called him in Bloomington, Ind., and told him that "two things are going to happen. One, it's going to be very tough in the committee room and, two, the stuff about Howard is going to surface."

Baker is a former dean of the Howard University Law School who was outspokenly critical of the educational level there. He resigned in May 1986 in a dispute over the qualifications of some members of the graduating class. Howard University President James Cheek said at the time he requested Baker's resignation because of "incompetence" and "insubordination."

Baker said Greene was not specific about how the Howard dispute would surface if he testified. But he said he took her to mean that it would be raised in the press rather than the committee room.