The 45-year-old music mogul won the award for the song "If I Rise" for Danny Boyle's film "127 Hours", a collaboration between Rahman and pop star Dido.
The Critics' Choice Movie Awards are bestowed annually by the Broadcast Film Critics Association (BFCA) to honour the finest in cinematic achievement.
The star-studded ceremony was held at the Hollywood Palladium. "The Social Network" was named the year's Best Picture and David Fincher won the Best Director honours for the film.
Hollywood's Colin Firth won the Best Actor award for his role in "The King's Speech" and Natalie Portman was declared the Best Actress for her performance in "Black Swan".
This is Rahman's second collaboration with Boyle after Mumbai-based underdog drama "Slumdog Millionaire".