Born in Edinburgh, Scotland, Graham began his career with Rangers, making his debut in the 5–3 away win against Shelbourne in the UEFA Cup first qualifying round first leg.

He settled in well at Torquay United, helping the Devon side retain their league status on the final day of the season in the crucial game at Barnet.

In July that year he signed permanently for Torquay and played a major role in turning the club's fortunes around, culminating in automatic promotion at the end of the 2003–04 season.

[7] He scored nine goals in seventeen appearances for Huddersfield Town, helping them to ensure a play-off place in League One, if not quite automatic promotion.

Graham was blocked from Wednesday's 2006 tour of the United States, visa restrictions due to a minor police offence nine years previously preventing his entry to the country.

[8] Wednesday accepted an undisclosed bid for Graham from Blackpool on 27 July 2006, but he turned down the move, instead joining Bradford City on a five-month loan deal.

On 21 March it was announced that Graham would be returning to the team bottom of the football league where he first made a name for himself, on a loan until the end of the season, at Torquay United.