The versatile midfielder, who can also operate in defence, teams up with former City player and coach Gary Owers at Twerton Park.
Murphy arrived at Ashton Gate in the summer of 2014 having been spotted by Brian Tinnion playing for Hereford United, where he had broken into the first-team.
Now the 19-year-old will temporarily return to non-League football with the Romans.
The deal will expire on Sunday, March 6th after a total of eight league matches.