Chambly, Quebec
A native of Chambly, Quebec, Robertson grew up in Somerville, Massachusetts, and attended Somerville High School and Worcester Academy. In 1914 and 1915, Robertson and his brother Jim Robertson played summer baseball for the Falmouth "Cottage Club" team in what is now the Cape Cod Baseball League. While Jim played first base, Harry was a catcher, and was reportedly a "fast and aggressive" player.