Barrow joint-manager Dave Bayliss told BBC Radio Cumbria: "He's experienced, knows the grounds and it's important to get people in who know the level.
"Jon gives us a presence up front, he's just become available and we moved quickly to get him."
Shaw began his career as a trainee with Sheffield Wednesday but enjoyed his best spell with Burton Albion where he scored 27 times in 86 games.
While with Crawley last year he scored five goals in 12 Blue Square Premier appearances.
He has made two appearances as a substitute for Rochdale this year but his first-team chances have been limited since his arrival at Spotland last July.
Source: BBC Sport
Source: BBC Sport