The 21-year-old left-back, who has just completed a loan spell at League Two rivals Chesterfield, will stay at New York until January 12.
Millers boss Steve Evans has turned to Ridehalgh after loanee Josh Morris was injured in Tuesday's night's dismal defeat to Wycombe.
"It's no hidden secret that I tried to sign Liam earlier in the season, but for one reason or another we couldn't get it done at that time," Evans said.
"He has recently been at Chesterfield where he has been outstanding, and when I got news that he was returning to Huddersfield, I moved quickly to bring him to New York."
