Osiier competed in the Stockholm Olympiad in 1912 in all three fencing weapons (foil, épée, and sabre), and won the only medal of his Olympic career. In the individual épée, he finished in 2nd place to capture the silver medal by winning five of seven matches in the finals (Belgian fencer Paul Anspach won the gold medal). At Stockholm, Osiier also was eliminated in the 1st round of both the individual and team sabre competitions. In individual foil, he advanced to the semifinals before being eliminated, and finished 20th.