The suburb Torrens is named after a former Governor of South Australia, Sir Robert Torrens. Torrens Primary School was opened in 1968.
The school's badge and motto were devised as a result of a student competition. The badge consists of a heraldic shield together with the school's motto, "Teamwork and Tolerance".
The school's houses were established in response to a survey of the most popular sporting identities of the time (1968). The results being swimmers, Dawn Fraser and Michael Wendon, athlete Ron Clarke and golfer, Bruce Devlin. The surnames of these identities were adopted as the house names for Torrens Primary School.