William A. Borders Jr., a prominent Washington lawyer who was convicted March 29 of conspiring with a federal judge in Miami to accept a $150,000 cash bribe from a man posing as a convicted racketeer, was sentenced here today to four concurrent jail terms of five years and fined $35,000.

Borders, a longtime District criminal lawyer who once headed the National Bar Association, an organization of black lawyers, was sentenced in a case that also involves U.S. District Judge Alcee L. Hastings. Hastings is challenging the court's authority to bring him to trial while he is a sitting federal judge. A trial date for Hastings has not been set.

At the sentencing, U.S. District Judge Edward T. Gignoux wondered aloud why Borders, whose career had brought him influence and prestige that extended throughout the Washington judicial system, jeopardized "his entire life's work" and the respect of his friends and peers to solicit a bribe from a man who he thought was a convicted racketeer seeking leniency from the judge who was to sentence him. Gignoux characterized the crime as "horrendous" and "inexcusable."

Borders, who once sought mercy for some of Washington's most notorious drug dealers and gamblers, stood in front of the bench today and asked for mercy on his own behalf.

"I stand before you a humble, broken person asking you to do what's best," Borders asserted in a quiet, restrained tone. Minutes later, he showed no emotion as Judge Gignoux ordered the maximum fine, in addition to a maximum five-year prison term for each of four charges. He ordered that Borders serve his sentence in a minimum security prison near his home in the District. Lawyers said Borders could be paroled after serving 18 months in jail.

"The public would be properly outraged if the court sanctioned a sentence that wasn't commensurate with the outrage imposed," said Judge Gignoux, who is from Portland, Me. He presided over the six-day trial after all federal judges in Miami recused themselves because of the alleged involvement of one of their colleagues--Hastings. The trial was moved here from Miami after Borders asked for a change of venue.

Borders, who was convicted of conspiracy to commit bribery, obstruction of justice and two counts of interstate travel to commit bribery, will remain free on $25,000 bond. His attorney, John A. Shorter Jr., who along with Atanta lawyer Marvin Arrington represented Borders, said he would appeal.

"It was a pretty good sentence," said Arrington, president of the Atlanta City Council. "But it's more than a slap on the wrist. Five years and a $35,000 fine is a whole lot of slappin'."

Borders was arrested last Oct. 9, the same day friends and associates from around the country had gathered in Washington to honor his leadership of the 56-year-old black bar association. He missed the party. One invited guest--Judge Hastings--chose to skip the affair, flying home hours after learning of the arrest of his long-time friend, according to testimony at Borders' trial.

Hastings faces conspiracy charges in connection with a bribe that Borders was convicted of accepting on Hastings' behalf from a man Borders believed to be one of two brothers convicted in Hastings' courtroom of racketeering. Hastings has maintained his innocence and has contended that since he is a sitting federal judge, he cannot be tried unless he is first impeached.

During the trial, the seven-man, five-woman jury heard 15 secret tape recordings, including three conversations between Borders and an FBI undercover agent and a telephone conversation between Borders and Hastings.

At one meeting with the agent, Borders pocketed $25,000 as a down payment on the bribe.

"The extent and scope of his corrupt scheme was almost breathtaking," said Justice Department attorney Reid H. Weingarten, arguing for a "severe sentence."

The government asserted that in exchange for the money Borders received from a man he believed to be Frank Romano, Hastings released $845,000 in assets that he had ordered forfeited by Frank and his brother, Thomas, and also promised to modify prison sentences he had imposed in the case.

A retired FBI agent, H. Paul Rico, 57, wore a body bug to three meetings with Borders, the first one on Sept. 12 when Borders said, "I think we can help you," and later wrote "$150,000" on an envelope he pulled from his pocket, the court was told.

That tape--plus a dozen others--made up most of the government's evidence against Borders and is expected to play an important role in any trial of Hastings. At another meeting, Borders promised that Hastings would refund the Romanos' forfeited assets, the court was told.

Later, the government contended, Hastings ordered his law clerk to draw up some forms, then phoned Borders to inform him that he had "drafted all those, ah, ah, letters, ah, for him." Borders subsequently was arrested in Arlington, Va.

Borders graduated from Howard University Law School and rallied support and campaign contributions for President Jimmy Carter's campaign. Carter appointed Borders to a commission that recommends persons for seats on the federal bench in Washington. Borders successfully fought a Reagan administration attempt to remove him from the post in favor of a Republican last summer, then resigned from the commission after his conviction.