Oleksandr Babor started his career in 1997 with
Desna Chernihiv the main club of the city of
Chernihiv. Here he played three seasons. In 2000 he moved to
Ros Bila Tserkva where he managed to play 37 matches and scored 2 goals. In 2004 he moved to Desna Chernihiv where he won the
2005–06 Ukrainian Second League. He also played for
Sokil Zolochiv,
Dnipro Cherkasy and
Mykolaiv. In 2009 he moved to Yednist-2 Plysky where he managed to win the
Chernihiv Oblast Championship in 2009, 2010 and 2011, he also won the
Chernihiv Oblast Cup in 2009 and 2010. In 2016 he moved to Frunzenets Nizhyn where he managed to win again the Chernihiv Oblast Championship and the Chernihiv Oblast Cup. After he played for
Avanhard Koryukivka and in
Kudrivka where he ended his career. ==Managerial career==