The centre-back had been given the role in recent weeks while Park Ji-Sung had a spell on the sidelines with a muscular injury.
However, despite the fact that the South Korean midfielder has returned to action, Redknapp has confirmed that Hill will remain his skipper.
"Clint is a great character, a good lad and a fantastic professional," Redknapp told the club's official website. "He leads by example and has been superb for me since the moment I walked through the door.
"You know what you're going to get from Clint when he plays and that's 100%. He puts his body on the line for the club and that's what we need. We are in a battle to stay in the Premier League and we need players like him."
Hill has made 89 appearances for the R's since his arrival on a free transfer in 2010.