The 20-year-old has yet to feature for the Hammers so far this campaign and heads to Plainmoor in search of first-team football.
During loan spells at Aldershot and AFC Wimbledon last season McCallum netted seven goals in 18 appearances and Gulls boss Alan Knill, whose side have lost five of their last seven games, is looking for the young forward to boost his misfiring side.
"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," Knill told the club's official website.
"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.
"He's been injured and now his fitness is good, but just needs games. He is a physical presence and an alternative option because you can't always pass it around people in the box.
"On Saturday against Mansfield, we put a lot of good balls into the box but it was quite difficult for our players to get on the end of it, so a bit more size always helps."