In the 100 metres competition at the 1908 Olympics, Robertson won his first round heat with a time of 11.4 seconds to advance to the semifinals. There, he lost a close race to countryman Nathaniel Cartmell, both clocking at 11.2 seconds and Cartmell winning by about a foot. The loss to Cartmell eliminated Robertson from advancing to the final. On the same day as his semifinal loss in the 100 meters, Robertson was eliminated in the preliminary heats of the 200 metres with a second-place finish in his heat. His time was 23.0 seconds, 0.2 slower than the winner's. He also participated again in the standing high jump competition but his result is unknown.