The 33-year-old Senegalese striker most recently played for Finnish football club Honka.
Kandji started his playing career at American club Atlanta Silverbacks in 2007.
He has also played at New York Red Bulls, Colorado Rapids, Greek team Levadiakos, HJK of Finland, Saudi Arabian Al-Faisaly and Inter Turku.
Sanat Naft, headed by Portuguese coach Paulo Sergio Bento Brito, sits 11th in Iran Professional Leahue (IPL) table.