Graciani started his playing career in 1981 with Club Atlético Atlanta in the Argentine 2nd Division. In 1983 the club were promoted to the Argentine Primera after winning the Primera B championship.
In 1984 Graciani was signed by Boca Juniors he went on to become their leading goalscorer of the 1980s, winning two international titles with the club.
In 1992 Graciani joined Racing Club but returned to Boca Juniors in 1993. By the end of his Boca Juniors career he had played 250 games for the club in all competitions, scoring 83 goals.
In 1994 Graciani played for Deportivo Español before dropping down a division to play for Atlético Tucumán and then Argentinos Juniors in the Primera B Nacional.
In 1997 Graciani was signed by Swiss club Lugano and his final club were Caracas FC in Venezuela in 1998.
After retirement as a player Graciani has gone on to work as a football coach, he was part of the coaching staff at Boca under Chino Benítez.