Spiteri was born in Attard. He started playing with his hometown Birkirkara at a young age. He then moved to St. Lucia where he won promotion to the Maltese First Division. Afterward, he joined Żabbar St. Patrick's and again won promotion to the Premier League. After two seasons he moved again to Birkirkara for two seasons. During these two seasons, Birkirkara won all major trophies in Malta and in the 1999–2000 season they were crowned league winners for the first time in their history. Spiteri ended up his career with Lija Athletic, where they won promotion for the Premier League in the 2000–01 season.