Robert Power competed in the 100 kilometres team time trial at the 1992 Barcelona Olympic Games as part of the Irish quartet alongside Mark Kane, Kevin Kimmage, Conor Henry and Paul Slane, finishing 17th in 2:14:32. From Dungarvan, Co. Waterford, Power earned his place on the team by finishing third in the 1992 Milk Rás – a result that secured his late selection for the Barcelona panel.

His Olympic involvement ended in tragedy: the day after the team time trial he was involved in a collision during a training ride in which he suffered a broken collar bone, prematurely ending his Olympic participation. Worse, the injury effectively ended his career as a serious cyclist, as Power never fully recovered from the collision. His Olympic experience was therefore both his finest moment in the sport and the occasion of the injury that cut short his career.