Liddell, 36, left Oldham in the summer due to personal problems and is hoping to repay the Millers for helping him through a tough period.
He told skysports.com: "I'm hoping to stay at Rotherham for as long as possible. I got the call from John Breckin who was at Oldham when I signed up there, and he told me to come down and show what I can do.
"Mark (Robins) has been great with me since I came and I am very grateful to both of them that they have allowed me to come and play some football.
"The summer has been very difficult for personal reasons and football has been the last thing on my mind, but Rotherham have allowed me to get focused on playing again and all I want to do now is do well for the Millers."