The 35-year-old left his role as player-assistant manager of National League South's Truro City by mutual consent last December.
Fallon, who scored six goals in 23 New Zealand appearances, has not played a competitive match since March 2016.
The signing completes player-manager Kevin Nicholson's search for a striker.
Fallon has had spells at a number of English clubs including Ipswich, Swansea and Swindon having started at Barnsley in 2000.
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National League side Torquay have signed former New Zealand international forward Rory Fallon on non-contract terms after a trial at the club.