Finch, 40, was one of eight men arrested in the past month who police allege "expressed desires to engage with sexual activities with children" in an adult phone chat service investigated by detectives.
The former State of Origin player was arrested at a home in San Souci in southern Sydney on Tuesday morning.
Police seized a mobile phone for forensic examination and Mr Finch was taken back to Kogarah police station.
There he was charged with five counts of using a carriage service to transmit or publish child abuse material.
