William A. Borders Jr. resigned yesterday from the D.C. Judicial Nomination Commission, four days after a jury in Atlanta convicted him of conspiring with a Miami federal judge to take a $150,000 bribe from a man he thought was one of two brothers convicted in the judge's courtroom of racketeering.

White House counsel Fred Fielding confirmed that commission chairman Frederick B. Abramson notified him late yesterday that Borders had sent Abramson a letter of resignation. Borders had been appointed to the commission by president Jimmy Carter. His replacement on the commission will be named by the Reagan White House.

According to Fielding, Borders said in the letter he was convinced that his innocence would be established when his conviction is reviewed by the federal appeals court. Borders said, however, that in the meantime, he thought it best to stand aside.

The nomination commission selects candidates for local trial and appellate judgeships and sends their names to the White House, which makes the final selection. The commission also names the chief judges of both courts.

Last summer, the Reagan administration tried to remove Borders from the commission in favor of its own candidate, Washington lawyer Philip A. Lacovara. Borders brought a lawsuit in the federal court to retain his seat and won. That case is now before the U.S. Court of Appeals.

On Monday, a U.S. District Court jury convicted Borders of conspiracy to commit bribery, obstruction of justice and two counts of interstate travel to commit bribery. The jury verdict was reached after only 65 minutes of deliberation, and followed a six-day trial. As part of its evidence, the prosecution played 15 secret tape recordings of conversations between Borders and an FBI undercover agent and a tape of a telephone call between Borders and U.S. District Judge Alcee L. Hastings in Miami.

The prosecution contended that Borders acted as a "middle man" for Hastings in the bribe scheme and took a $25,000 cash down payment from the undercover agent, who was posing as convicted racketeer Frank Romano. In exchange for the payoff, the prosecution charged, Hastings returned $845,000 that had been forfeited by Romano and his brother, Thomas, and planned to reduce prison sentences he had imposed on them.

Hastings is expected to be tried in Miami.