Elorza defeated City Council President Michael Solomon in Tuesday's primary.
The 37-year-old Elorza grew up in Providence after his parents immigrated to the U.S. from Guatemala. He has not held elected office, but served as an appointed part-time judge on the city's housing court. He is a tenured professor at Roger Williams University School of Law.
The race now becomes a three-way contest pitting Solomon and Republican Daniel Harrop against Cianci, who is running as an independent.
Cianci was forced from office twice due to felony convictions, the most recent in 2002. He was convicted of racketeering conspiracy for presiding over widespread corruption in City Hall.