He was jailed for nine years after officers discovered the recording during the forensic examination of his computers. His victim was an eight-month-old girl, who was taken into care with her three siblings.
He was one of 300 suspected paedophiles arrested in Scotland since April 2013.
Police Scotland revealed the horrific crime as UK-wide figures were released.
A six-month operation carried out by the National Crime Agency (NCA) caught 600 suspected paedophiles - 13 in Scotland.
As reported in later editions of last night's Evening Times officers swooped on properties across the Britain during that operation.
It targeted internet users who access child abuse images and has already led to charges for serious sexual assault.
The NCA, which led the operation, confirmed 660 suspected paedophiles, including teachers, doctors and Scout leaders, had been arrested nationwide.
Detective Superintendent Steven Wilson, specialist crime division cybercrime unit, said: "Police Scotland has worked tirelessly to proactively utilise all available new technology to combat the threats posed by online offenders, bring them to justice and protect those who are at risk of falling victim to abuse and exploitation.
"Those who believe that the internet offers anonymity to exploit children should understand that there is no hiding place, every contact leaves a trace."
Detectives said the investigation, involving 45 forces, led to hundreds of children being "safeguarded".
The NCA stressed that none of those arrested is a serving or former MP or a member of the Government. But officials did confirm that suspects include care workers, former police officers and 39 registered sex offenders.
Some are workers who had access to children through their jobs and had no previous contact with police.
Officers searched 833 properties and examined 9172 computers, phones and hard drives.