He attended St. John Fisher Catholic elementary school and Pope John Paul II Catholic Secondary School in Scarborough, Ontario. As a midfielder he began playing football for the renowned North Scarborough Soccer Club, known for producing international players such as Julián de Guzmán formerly of Deportivo de La Coruña, Jonathan de Guzmán of Feyenoord, Atiba Hutchinson of F.C. Copenhagen and Dave Simpson of Sparta Prague. From there he went on to Erin Mills Soccer Club, one of Canada’s leading clubs that also produced players such as Dave Simpson. After which he earned an Athletic Scholarship to the University of Detroit Mercy where he was named Horizon League player of the year and offensive player of the year in 2005 on the way to leading the team to its first ever Horizon League Championship. He is the 4th All-Time top scorer in the History of University of Detroit Mercy. Ornoch began his professional career with a brief stint with the Mississauga Olympians in the Canadian Professional Soccer League in 2002. He made his debut for the club on 4 October 2002 against the Vaughan Sun Devils coming on as a substitute for Darren Tilley.

In 2008 Andrew went on to sign a 4-year contract with Esbjerg fB in the Danish Superliga where he joined fellow Canadians Atiba Hutchinson of Copenhagen and Issey Nakajima-Farran of Nordsjælland.

On 30 August 2009 he joined Dutch club Heracles Almelo, a former club of another fellow countryman, Rob Friend. On 26 August 2010, Ornoch joined Dutch Jupiler League club BV Veendam and scored his first goal in his second appearance versus Emmen on 3 September 2010. It was heavily rumoured that Ornoch was set to sign for Toronto FC of Major League Soccer prior to the 2011 season. However, in late January it was released that the deal fell through due to Aron Winter, the coaches lack of interest. Several sources say that Ornoch was upset by the decision, claiming that TFC advised him to buy himself out of his contract in Europe before pulling an implied offer off the table.

After a brief stint in the Canadian Soccer League with Mississauga Eagles FC Ornoch returned to the Netherlands to play in the Eerste Divisie with Telstar. He made his debut for the team on 5 August 2011 against FC Dordrecht scoring one goal, the game ended in a 3–0 victory for Telstar.