Judge Robert H. Bork, whose nomination to the Supreme Court set off an extraordinarily divisive political battle, will resign from the federal appeals court here next month, the White House announced yesterday, to answer what he described as a "campaign of misinformation and political slogans" that doomed his chances for confirmation.

Bork had considered resigning even before his nomination last July to the high court, according to several acquaintances, who said he is bored by the dry, predominantly regulatory caseload at the D.C. Circuit, where he has served for six years. He had not hired clerks for the coming term.

"It was a rare case, not a regular case, that engaged him {on the D.C. Circuit}. That's one reason he was so eager to get on the Supreme Court," said a Bork friend who discussed the resignation with him.

In a two-page letter dated Jan. 7 and released yesterday by the White House, Bork said that leaving the court is the only way he can publicly challenge what he views as a dangerous trend toward allowing judges to "set the social agenda for the nation" -- a concern he has advanced for 25 years.

President Reagan, in a letter responding to Bork, called his defeat a "tragedy for our country. All Americans are the poorer today for not having your extraordinary talents and legal skills on the high court."

Bork's nomination to fill the vacancy created by the retirement of Lewis F. Powell Jr. was widely viewed as an effort by Reagan to tip the balance of the court to the right and implement the conservative social agenda that he has had limited success in moving through Congress. As such, it mobilized liberal and conservative groups to view it as a legal armageddon.

Bork's nomination was rejected by the Senate on Oct. 23 by a vote of 58 to 42, the largest vote in history against a Supreme Court nominee. Reagan's second nominee to fill the vacancy, D.C. federal appeals court Judge Douglas H. Ginsburg, withdrew after disclosures that he had used marijuana while a professor at Harvard Law School.

Reagan's third appointee, appeals court Judge Anthony M. Kennedy of Sacramento, Calif., who is seen as a mainstream conservative, is expected to win confirmation easily shortly after Congress reconvenes this month.

Bork's decision to resign was closely held in the administration. It was known only to a handful of White House officials and at the Justice Department only to Attorney General Edwin Meese III and his top aide, William Bradford Reynolds, the key champions of Bork's nomination.

Sources said Bork wanted to guard news of his departure until the release of his resignation letter, which puts his move in the context of advancing a philosophical struggle rather than a retreat. The timing of the announcement surprised his fellow judges, since Bork was scheduled to hear arguments through March. Bork said one reason for the timing of his resignation is that he wanted to give Reagan time to nominate his successor.

"I wish to speak, write and teach about law and other issues of public policy more extensively and more freely than is possible in my present position," Bork said in his letter to Reagan. " . . . I had considered this course in the past but had not decided until the recent confirmation experience brought home to me just how misfocused the public discourse has become."

Bork has been negotiating to become a fellow at the American Enterprise Institute, a conservative think tank with which he was affiliated several years ago. According to a friend, he also plans to practice law part-time and to teach a course at a law school, possibly in the Washington area.

Bork, a former Yale Law School professor known for incendiary rhetorical attacks on liberal jurisprudence, lashed out last month against his opponents in a speech to the Law Club of the City of Chicago. He said the campaign against his high court nomination "set record lows in mendacity, brutality and vulgarity."

In the speech, reported by the Chicago Tribune, Bork said he was most angered by being portrayed as insensitive to blacks. He called it "a lie . . . but the lie took hold." Bork was solidly opposed in the Senate by southern Democrats, many of whom were elected with a majority of black votes.

Bork, who granted numerous interviews to news organizations during his confirmation fight, refused to take reporters' calls yesterday.

The appeals court judge will not be alone in challenging those who opposed his nomination. His son, Robert Bork Jr., an associate editor at U.S. News and World Report, is writing a book on the political struggle that resulted in his father's defeat.

Judge Bork, an antitrust scholar when he joined the Yale Law School faculty in 1962, began delving into constitutional law and became a champion of the conservative view that judges must adhere to the "original intent" of the framers of the Constitution and not to their own vision.

He wrote widely that the Supreme Court had overreached in declaring a constitutional right to privacy, in protecting speech beyond that related to political freedom and in extending the 14th Amendment to protect women and other groups besides racial minorities.

While at Yale, he also wrote that Congress had overstepped its authority in such landmark legislation as the Civil Rights Acts of 1963 and 1964. He called the Public Accommodations Act of 1963, and its requirement that proprietors serve blacks as well as whites, "a principle of unsurpassed ugliness."

Bork's conservative views attracted the attention of then-President Richard M. Nixon, who made him solicitor general in 1973. Several months later, Bork came to national attention as the "executioner" who carried out Nixon's order to fire Watergate special prosecutor Archibald Cox in what became known as the "Saturday Night Massacre."

At his confirmation hearings last September, Bork softened several of his most controversial stands, prompting opponents to attack his credibility and accuse him of a "confirmation conversion."

"What should have been a reasoned national debate about the role of the courts under the Constitution became an essentially unanswered campaign of misinformation and political slogans," Bork wrote in his resignation letter. "If, as a judge, I cannot speak out against this attempt to alter the traditional nature of our courts, I think it important to place myself where I can."