The R's have picked up just one victory in eight league games and were left frustrated on Sunday after suffering a late 3-2 defeat at the hands of Liverpool.
Recently, rumours emerged suggesting that Redknapp's time at the club could be up, but Bothroyd is backing the former Tottenham Hotspur boss to turn the club's fortunes around.
Bothroyd wrote on Twitter: "I'm sure Harry is the right man for the job ! I hate when I see managers get sacked after the first sign of trouble . Come on you R'ss."
The 32-year-old spent two years playing for QPR before moving to Muangthong United in Thailand in January.