Cansu Özbay started her volleyball career in Göztepe than continued in the youth development team of Arkas Spor at her hometown in İzmir.

[2] In January 2015, Özbay was loaned out from her club Beşiktaş JK to Nilüfer Belediyespor in Bursa, where she played the second half of the 2014–15 Turkish Women's Volleyball League season.

She was awarded the title of "Best Setter" of the 2017–18 season's final series.

[7] Özbay participated at the 2016 FIVB Volleyball Women's Club World Championship held in Metro Manila, Philippines, where her team Vakıfbank Istanbul placed third.

The next year, her team became champion of the 2017 FIVB Volleyball Women's Club World Championship in Kobe, Japan.