An Arlington General District Court judge yesterday found the director of Washington's Islamic Center guilty of marrying a Virginia couple without legal authorization.

Muzzammil H. Siddiqi, 38, was fined $50 after Judge Thomas R. Monroe found him guilty of conducting a marriage ceremony last Nov. 7 without the license required by Virginia law. Monroe delayed ruling until March 1982 on charges that Siddiqi performed two other allegedly illegal marriages.

According to court documents, Siddiqi performed marriages on Nov. 7, Dec. 21 and Dec. 25 of last year. Court documents recording the ceremonies that supposedly were signed by Siddiqi indicate the director was bonded, or legally authorized, to perform weddings in Virginia.

The documents list Siddiqi as bonded in Arlington in 1977, 1976 and 1973. But other court documents show that Siddiqi did not obtain bonding in Arlington until July 22 of this year, after the marriages were performed.

Virginia law requires that clergymen obtain a Circuit Court order permitting them to perform wedding ceremonies in the state.

Arlington assistant prosecutor William A. Nunn III said the marriages performed by Siddiqi apparently are valid, due to a "saving statute" that provides that an illegally performed ceremony is not void if the couple involved did not know that the person who officiated lacked proper authorization.

The charges in the illegal marriage case grew out of a federal Immigration and Naturalization Service investigation of the Islamic Center on Massachusettes Avenue NW. Referred to Arlington officials, the case was then brought to trial in the county court.