Senior Circuit Court Judge Franklin P. Backus said yesterday he will appoint an independent prosecutor to investigate possible irregularities in operations of bingo games in Alexandria.

Commonwealth's Attorney William L. Cowhig requested appointment of the special prosecutor Wednesday after several City Council members had accused him of having a conflict of interest in any bingo investigation because he had once organized bingo games himself.

Cowhig said yesterday that he had reviewed the proposed order appointing the prosecutor and that the "language . . . was agreed upon between the judge and myself." The special prosecutor, he said, will have independence to pursue the investigation.

"There is no restriction on the power or scope of the special prosecutor," Cowhig said. Backus refused to confirm or deny this last night.

Earlier yesterday Alexandria officials expressed concern over language in Cowhig's letter to Backus asking for appointment of on independent prosecutor that specifically stated the prosecutor could investigate possible misdemeanors.

Officials such as Police Chief Charles T. Strobel, however, had urged that the prosecutor have authority to bring felony charges for violating Virginia's gambling laws.

"If the bingo is a cover for a more ingrained gambling operation, then the special prosecutor will not be effective" if he is restricted to prosecuting misdemeanor charges, Strobel said yesterday.

Cowhig explained yesterday that he had cited the misdemeanor section of the state code in his letter Wednesday because that was the only section that specifically mentions bingo.

Bingo was legalized in Virginia in 1973 and shortly thereafter the Montessori School of Alexandria, Inc., which had been in financial difficulties since its founding in 1970, decided to run nightly bingo games to raise money.

Through the years, the Montessori game, now held three times weekly at 350 S. Pickett St., has proved to be by far the most successful game in the city. In 1977, for example, $549,321 was taken in at the door; $307,836 was spent in overhead and prize money, and $241,485 was returned to the school fund, a profit for the tax exempt organization of 43.9 percent.

"Bingo has been a miracle for us," said school director Dirgham Salahi.

The school has been able to pay off nearly all its original $155,000 mortgage, purchase a 10-acre parcel of land in the Franconia section of Fairfax County for $110,000 and put away enough cash to start preparations for a $500,000 high school on the site, the first such Montessori high school in the country, Salahi said.

The Montessori profits of 43.9 percent are consistent with the range realized by other licensed bibgo games in the city, a study of official figures show. However, they are in stark contrast with the profits of only 3.8 percent realized by games held at a bingo parlor at 3819 Mount Vernon Ave., according to city records.