Born in Romania, Sorin Stoica played soccer in his youth at a high level but quit at age 19 to become a police officer. He quit after five years, and in the year 2000, he and his wife moved to the United States, settling in Cleveland, Ohio.

As he already held a Romanian referee license, it was a natural progression to take the steps to get certified in the U.S. His first assignment in the Ohio youth leagues was in a State Cup match as an assistant referee to Chris Penso, now a well-known name in the referee world. Stoica would eventually join Penso on the MLS referee roster when he was selected in 2012.

Stoica made his MLS refereeing debut in a match between the Houston Dynamo and the New York Red Bulls. In 2015, he became the first official to send off world famous star Kaká during a match for the first time in his long playing career. Also in 2015, he served as the fourth official to Ismail Elfath for the MLS All-Star Game, and performed the same role in the U.S. Open Cup Final in 2016.

After officiating 85 MLS matches from 2012 to 2018, along with nearly a hundred matches as a fourth official, Stoica began serving chiefly as a video assistant referee in well over 100 matches up to the present day.