Cansu Özbay, born on October 17, 1996, in İzmir, came through the youth system of Arkas Sports Club. In 2014, she transferred to Beşiktaş and played for Nilüfer Belediyespor in the second half of the same season. The talented setter completed the 2015–2016 season with Beşiktaş and transferred to VakıfBank at the beginning of the 2016–2017 season. Wearing the yellow-black jersey, Cansu Özbay won 3 FIVB Club World Championships, 4 CEV Champions League titles, 3 Sultanlar League championships, 3 Turkish Cups, and 2 Super Cups.
Having played for all youth levels of the national teams, Cansu Özbay won bronze medals at the 2018 FIVB Volleyball Nations League and the 2019 Women's European Championship with the Turkey Women’s National Volleyball Team. The 1996-born player was part of the squad that secured a ticket to the 2020 Tokyo Olympics by finishing first in the 2020 Tokyo Olympic Qualification Tournament, and she competed in the Olympic Games. Cansu Özbay was the setter of the national team in the 2023 FIVB Volleyball Nations League and the 2023 CEV European Championship, both of which ended with a championship victory.