The 20-year-old had spells at AFC Wimbledon and Aldershot Town last season, scoring multiple goals at both clubs.
Torquay manager Alan Knill told the Gulls' official website: "We hope he is the missing jigsaw piece and you don't have to be a football genius to know we're missing a little bit at the top end of the pitch.
"Paul is something different. He scored goals last year for Aldershot and Wimbledon, and actually scored here for Wimbledon, and we're very thankful to West Ham for letting him out."
McCallum will be available for this evening's League Two match at Burton Albion.