Evan Horwood suffered a groin injury in Rovers' 2-0 Capital One Cup defeat to Stoke in midweek, while Danny Holmes missed training this last week due to illness.
But the 22-year-old Ridehalgh, who includes Rotherham and Swindon among his former employers, has been brought in to Prenton Park ahead of their League One fixture at home to Port Vale on Saturday afternoon.
"Evan Horwood's groin injury has left us short at left-back so I'm pleased to add Liam to our squad," boss Ronnie Moore told Tranmere's official website.
"He has League One experience and played 36 times for two good League Two sides last season and helped Rotherham get promoted.
"He's a defensive-minded left-back but will get forward and support the winger.
"There were a lot of young inexperienced players out there but Liam fits the bill for us because of the number of games he has played."