WASHINGTON (AP) _ Judge Robert H. Bork, President Reagan's choice for the Supreme Court, is sure to face tougher questioning over a Watergate-era episode than he did when he was confirmed to the federal appeals court here in 1982.

Bork, a scholarly conservative, is best known nationally for his role on Oct. 20, 1973, when as solicitor general he fired Watergate special prosecutor Archibald Cox on orders of then-President Nixon after higher-ranking Justice Department officials refused.

The incident is not expected to be an insurmountable obstacle to Senate confirmation of Bork as successor to newly retired Justice Lewis F. Powell on the nation's highest court.

But even so, the Senate Judiciary Committee - run by Republicans in 1982 but now controlled by Democrats - undoubtedly would grill Bork extensively this time around.

''It will be the subject of some careful consideration,'' said a Democratic committee aide who requested anonymity. ''It will certainly play a role.''

Alluding to the Reagan administration's problems with the Iran-Contra affair, he added, ''The current climate may serve to rejuvenate interest'' in the Watergate scandal.

Senate Majority Leader Robert C. Byrd, D-W.Va., has said that because of the Watergate incident Reagan ''would be inviting problems'' if he chooses Bork. But Byrd also conceded that Bork would be confirmed.

Other Democrats on the Judiciary Committee, including Chairman Joseph R. Biden Jr., D-Del., and Sen. Edward M. Kennedy, D-Mass., have said that hostile questioning awaits any Supreme Court nominee picked solely because of conservative ideology.

Bork, testifying Jan. 27, 1982 before the committee, said he acted honorably in carrying out the order to fire Cox in what became known as the Saturday Night Massacre.

''On the one hand, there was no threat to the (special prosecutor) investigations from the discharge (of Cox) and no threat to the processes of justice,'' Bork said. ''On the other hand, I preserved an ongoing and effective Department of Justice.''

He added, ''The only thing that weighed against doing what I did was personal fear of the consequences. And I could not let that, I think, control my decision.''

The incident was triggered by Nixon's order to then-Attorney General Elliott Richardson to fire Cox. Nixon was engaged in a court battle with Cox over the special prosecutor's bid to obtain White House audio tapes.

Richardson and William Ruckelshaus, second in command at the Justice Department, resigned rather than dismiss Cox.

But Bork said both of his superiors felt bound by promises they made to the Senate not to fire the special prosecutor.

As solicitor general - the administration's top courtroom lawyer who guides and argues appeals to the Supreme Court - Bork was the third ranking Justice Department official.

A former Yale University law professor, Bork testified in 1982 that the entire Justice Department structure would have crumbled had he refused Nixon's order.

''There was nobody after me in the line of succession, nobody,'' Bork said. ''If I resigned, there was simply nobody who stepped into that position.''

He said that if he had quit Nixon would have named an acting attorney general from among the White House staff. Then, he said, there would have been ''massive resignations from the top levels of the Department of Justice ... and (it) would, I think, have effectively been crippled.''

Bork said he had discussed ''the whole ruckus'' with Ruckelshaus and he said they agreed that, unlike his superiors, Bork was not bound by their promise to retain Cox.

''I had made no such representations and therefore I had a moral choice to make free of those problems they had,'' Bork testified.

Moreover, he continued, he retained Cox's staff and picked Leon Jaworski to be the new special prosecutor.

''They were independent. They remained independent. They went to court,'' Bork said. ''The investigations went forward with the results we all know and are now a part of American history. At no time was there any threat to the integrity of the processes of justice.''

When Bork finished his remarks, Sen. Max Baucus, D-Mont., said: ''I think your statement today helps explain all of that and I appreciate that statement very much.''

Bork was confirmed unanimously by the Senate to be a judge on the U.S. Circuit Court of Appeals here.

Richardson says Bork acted properly in 1973 and endorses him as a worthy candidate for the Supreme Court.

''I think he would be an outstanding member of the court,'' Richardson said recently. ''Bork deserves a lot of credit for standing up to Nixon and telling him to appoint another special prosecutor.''