The 23-year-old moved to the Robins for an undisclosed fee in January from Brighton & Hove Albion.
Barker has made two starts since his move to the County Ground and only featured as a substitute this season.
"George will give us pace up front and will cause opposition defenders problems," Tranmere manager Rob Edwards told the club website.
"We're grateful to Mark Cooper and Swindon Town for letting George come to us."
Barker is available for Saturday's game against Plymouth as he looks to help Rovers move away from the League Two relegation zone.
Tranmere Rovers have signed Swindon Town striker George Barker on a one-month loan deal.