Alexandria prosecutor William L. Cowhig was acquitted by a jury yesterday of a charge that he asked for and received $32,000 in bribes from the city's leading bingo operator.

Cowhig, the only incumbent commonwealth's attorney indicted in the history of Virginia, showed little emotion as the verdict was read by assistant Alexandria Circuit Court clerk Stephen Jamgochian at 2:05 p.m. Cowhig's friends and supporters, who were apcked into the second-floor courtroom, erupted with cheers, applause and sobs as Jamgochian read the words "not guilty."

One juror said after the trial that the "lack of credibility" of bingo operator Dirgham Salahi, the chief witness against Cowhig, was the major factor in the verdict.

The juror, who asked not to be named, said that the failure of the prosecution to fully document its allegation that Cowhig needed the alleged bribe money because he was living beyond his means also weighed in the decision.

At a victory celebration afterward, Cowhig said the verdict was "just."

As the jury's decision was announced in the courtroom, chief defense lawyer Louis Koutoulakos hugged cocounsel Leonard B. Sussholz, who burst into tears.

Special prosecutor Edward J. White, an Alexandria attorney named last April 21 to investigate potential abuses in the city's lucrative bingo operations, including allegations of Cowhig's own involvement, left the rowded courtroom without comment.

The jury of seven men and five women had deliberated for more than 13 hours, from shortlyafter 2 p.m. Wednesday until they were sent home by Circuit Court Judge Percy Thornton Jr. at 3 a.m. yesterday. They returned at 1 o'clock yesterday afternoon and indicated that a verdict had been reached about half an hour later.

After a short delay while Thornton was located and called back from lunch, the jury's decision was announced.

Koutoulakos said later that "based on the evidence Salahi gave police, I think they had to bring an indictment. But I don't know how you could convict anyone on his testimony."

Cowhig, 53, in his second term as Alexandria's elected chief prosecutor, stepped aside from the the $42,500 job following his Aug. 3 indictment by a city grand jury on one count of bribery and two counts of illegal gambling connected with bingo operations. He is scheduled for trial on the gambling charges starting Jan. 22 and March 5.

If Cowhig had been convicted yesterday, he would have faced a sentence of from two to 10 years imprisonment. The gambling charges carry a possible sentence of up to 10 years in prison and a $20,000 fine for each count.

Cowhig has said he will not return to office until the charges are resolved. He continues to draw his salary.

The bribery indictment handed down last August charged that Cowhig had taken bribes totaling $32,000 over a 16-month period from Slahi, whose Montessori School of Alexandria was sponsoring allegedly illegal bingo games.

Salahi testified during the seven-day trial that he made cash payments of $500 a week to Cowhig from Jam. 4, 1977, to May 1, 1978, in order to buy "peace" from "harassment" by the prosecutor, who he said had threatened repeatedly to shut down the Montessori games.

After he began the payments, Salahi alleged, Cowhig's threats stopped and the games, which Salahi called the lifeblood of his school, were allowed to continue.

Defense lawyers made Salahi's credibility a major theme of their trial strategy. Salahi, who testified last week that he had once lied to police was granted immunity from state and federal prosecution in exchange for his testimony.

During the trial, defense attorney Koutoulakos called Salahi a "liar" and a "crook" who had "set up" Cowhig in revenge for a 1976 investigation by Cowhig of Salahi's bingo games.

Sussholz also attacked the motivations of Virginia State Police investigator Coy Ivy, who had conducted the 1976 investigation for Cowhig, and who investigated Cowhig's personal finances on behalf of the prosecution for the bribery trial.

According to Sussholz, Ivy was "mad" that Cowhig had never prosecuted Salahi, Although Cowhig had turned the matter over to the federal internal Revenue Service, which had declined to act.

Jury sources indicated yesterday that Ivy's investigation had not fully documented, in their view, the prosecution's contention that Cowhig was living beyond his means during the period of the alleged bribes.

One source wondered why the prosecution had not mentioned certain Cowhig bank accounts, each of which contained several thousand dollars.

Some jurors also indicated doubt about a prosecution claim that an $1,820 monthly mortgage payment Cowhig was making on a small Bahamian hotel he owned was a major drain on Cowhig's finances.

The defense presented its version of Cowhig's finances through an analysis by Alexandria accountant Frank B. Higdon, who became a key defense witness.

Judge Thornton, who is usually assigned to the Prince William County Circuit Court bench, was appointed by the Virginia Supreme Court to hear the case after all three Alexandria Circuit Court judges excused themselves because of their personal acquaintance with Cowhig.

The trial was often rancorous, as prosecutor White, and defense attorneys Koutoulakos, Sussholz, James M. Lowe and William B. Moffitt battled for legal advantage. The bitterness spilled into the courthouse hallways as the jury deliberated Wednesday night, when Moffitt and Ivy scuffled briefly and Sussholz punch White on the shoulder.

After the verdict Sussholz told the Associated Press that Cowhig had been "pillotied" by the media, and charged that The Washington Post, The Washington Star, and the Alexandria Gazette had done everything posible "so that Cowhig wouldn't get a fair trial."

State Sen. Wiley Mitchell (R-Alexandria) said yesterday he did not expect Cowhig's acquittal to dampen efforts to reform laws governing bingo operations.

Mitchell said the abuses that have come to light and the conviction of several other persons in Alexandria involved in illicit bingo operations "have created a climate for reform of the laws."

A bingo reform bill has been drafted for consideration by the 1979 legislative session, and Wiley said he does not expect any major difficulties in its passage.

Senate Majority Leader Adelard L. Brault (D-fairfax) said in an interview that Cowhig's acquittal "will have no effect at all" on the reform movement.

Aleandria City Councilman Donald C. Casey, a Democrat, said he was glad the bribery trial was over and that he felt the parties involved "got a complete airing" of the case. "The jury has decided, and that's it. The man's innocent," he said. CAPTION: Picture 1, Alexandria prosecutor William Cowhig leaves court with a supporter, Peggy Hogge. AP Picture 2, William Cowhig was sketched as he waited for jury to come in with verdict. By Joan Andrew for The Washington Post; Pircute 3, William Cowhig is flanked at victory party by lawyers Leonard B. Sussholz, left, and Louis Koutoulakos. By Gerald Martineau-The Washington Post