Judge Albert B. Fletcher Jr. of the U.S. Military Court of Appeals was convicted yesterday of soliciting an undercover Fairfax County police officer to commit a homosexual sex act last October in a park along the George Washington Parkway.

The 12-member Fairfax Circuit Court jury, which deliberated 5 1/4 hours over two days, recommended the 59-year-old federal judge be fined $500. Sentencing was set for March 15.

Fletcher, a former state judge from Kansas who was named to the three-member military court by President Ford, can appeal the conviction, but his lawyer said no decision has been made on that issue. Fletcher is the second active federal judge to be convicted of a felony in the last decade, according to Justice Department officials.

Whether his conviction will mean his removal from the bench was unclear yesterday. Fletcher can be dismissed by President Reagan only for "neglect of duty or malfeasance in office or for mental or physical disability," according to federal law.

Officials could not say yesterday whether his conviction falls under those provisions. White House spokesman Mark Weinberg said: "We have no comment and I would not anticipate there being any."

Fletcher, one of 16 men arrested in what police said was a crackdown on homosexual activity near the Belle Haven Marina south of Alexandria, had maintained he was innocent. He acknowledged accompanying the officer who arrested him to a car after he claimed the officer propositioned him.

The judge told the jury he hoped to engage the man in conversation about homosexual relationships in order to get information to help him decide a case involving homosexuals that was before his court.

"I thought we would walk over to the car and talk," Fletcher said on cross-examination. "To be honest, I made a mistake. I wouldn't do it again. I was hoping to garnish some information."

Since his arrest Oct. 24, Fletcher has not sat on any new cases brought before the court.

The judge, his wife and youngest daughter all sat impassively as the clerk read the verdict. Fletcher turned to face the grim-faced jurors as the clerk polled each one to verify the verdict.

After the courtroom was cleared, Fletcher embraced his wife, his daughter and his attorney, Steven Pickard, and all four appeared to be crying. The judge and his lawyers declined to comment.

Assistant Fairfax prosecutor Raymond F. Morrogh told the jury that Fletcher's testimony conflicted sharply with the account of the arresting officer and "doesn't make sense." In his final argument Morrogh noted that the undercover officer, Albert J. Roganti, had testified that the judge propositioned him and that the judge had accompanied the officer to a car.

The prosecutor said later that Fletcher had rejected a plea bargain in which he would have pleaded guilty to a misdemeanor.

Fletcher, who lives in Fairfax, was appointed to the federal court, which hears appeals of cases tried in military courts, in 1975. He served as its chief judge from 1975 until 1980; his term will expire May 1, 1986.

Fifteen other men arrested during the same police operation all pleaded guilty to a lesser misdemeanor charge, and most were fined $100.

The other sitting federal judge convicted recently of a felony committed while in office is U.S. District Court Judge Harry Claiborne, who was found guilty last August in Reno of two counts of tax evasion.