He played for the Tigers on Tuesday night in the Gloucestershire Senior Cup against Cheltenham Town.
Edge was released by Evo-Stik League South Premier side Hereford FC at the end of last month after failing to force his way into the starting eleven.
Gloucester-born Edge, 24, was on Cheltenham Town's books before being signed by Arsenal in July 2009 as a 15-year-old for a reported six-figure fee.
He then moved in August 2011 to West Bromwich Albion, where he spent a season before spending a year at the Nike Football Academy.
Edge joined Gloucester for the first time in August 2013, only to then sign for Cirencester Town two months later.
He joined Hereford United in December 2013 before returning to Cirencester in the summer of 2014.
A move to Weston-super-Mare followed in October 2014 before signing for the Bulls in July 2016.