The Ivory Coast international uploaded a video of a goal he scored for the Istanbul giants while at Galatasaray.
Drogba spent two seasons at Galatasaray and scored 20 goals in 53 games before joining Chelsea in the summer.
The Ivory Coast international won the Süper Lig, Turkish Cup and reached the quarter-final of the Champions League while at the Lions.
Drogba provided two assists and seven goals in 40 appearances for Chelsea last season before moving to the MLS over the summer.
The experienced striker has hit the ground running in the MLS scoring 11 goals in 11 appearances for the Canadian based side.