The stock rose to as high as 34.5c, well above its 20c initial public offering price.
Shares closed at 29.5c.
Taylor Collison was lead manager to the oversubscribed offer, which saw 50 million shares issued.
Torrens' primary focus will be its 1609sq.km tenement package in central Victoria, where it plans to spend more than $5 million over the next two years.
The Mt Piper gold project is just 30km southeast of Kirkland Lake Gold's Fosterville mine, while the Club Terrace gold project is in eastern Victoria.
The company also holds the Elizabeth Creek copper-cobalt project in South Australia, which is being funded by farm-in partner, newly listed Coda Minerals.
The Laloki copper-gold volcanogenic massive sulphide project in Papua New Guinea is considered a high-grade opportunity close to infrastructure.
"The strong investor interest in Torrens' IPO and its associated exploration portfolio represents a strong endorsement of our assets and management team and the strength of our core strategy - which is to discover and develop gold and copper deposits in Australia and PNG," Torrens non-executive chairman Bill Bloking said.
Steve Shedden is managing director, with Mike Collings and Richard Grauaug as non-executive directors and David Palumbo as chief financial officer and company secretary.
Bloking is also the largest shareholder with 10.1%. Shedden holds 6.5%.