Graham Bencini's senior playing career started with a championship with his first Premier Division side Sliema Wanderers. Graham came to prominence in the 1996/97 season playing in defence for Naxxar Lions. After two seasons with Naxxar he moved to Birkirkara where he enjoyed a great deal of success. He was a regular in the team that brought the first league championship to Birkirkara in 1999/00. With Djorde Pintac and Michael Spiteri, he was part of a defensive trio in front of the Birkirkara keeper Robert Savic that managed to keep seven consecutive clean sheets. He also featured in several cup finals, including the ground-breaking triumphs (Birkirkara's first major honours in their history) in the Super 5 Cup and Lowenbrau Cup in 1998/99. 

Bencini moved on to Hamrun Spartans where he spent the good part of 3 years before obtaining his free release and joining Sliema W. Graham notched a handful of premier division appearances with this team and won his third championship.

In the off-season of 2004 he moved to Floriana. But Bencini never managed to string a sequence of consecutive appearances in Willie Vassallo's side and it was a matter of time before he left this club. He obtained his release in the January 2005 transfer window and followed his ex-team-mates Bizu (from Floriana) and Daniel Dengaky (from Hamrun) to Ghajnsielem.

Graham had shown early promise and made it to the Under/21 squad where he appeared in one match. He made his debut for Malta's senior side in a friendly match against Bosnia at Ta' Qali on the 27th of January, 1999 still short of his 23rd birthday. Graham came in as a late substitute for Carmel Busuttil. Malta won that match 2-1. His next appearance, also as a second half substitute (for Gilbert Agius), was a 0-3 home loss to Yugoslavia on February 10, 1999 a European Championship qualifier. After another appearance, he did not feature again in the national team.

Bencini featured prominently in Ghajnsielem's 2004/05 championship winning team, often marking the opposition's main striker out of the game. The Blacks did not suffer a league goal from open play with Graham in the side.