Paul Gorman, 46, befriended the girl and offered her Â£40 to supply indecent images, which she took on a mobile phone in toilets at her school.
Police were called after a family friend spotted suspicious Facebook messages between Gorman and the girl.
Officers later found images of children being sexually abused on a computer at his home in Kilbirnie, North Ayrshire.
Midway through his trial at Kilmarnock Sheriff Court, Gorman admitted taking or making indecent images at a house in Dalry in May 2014.
A jury found him guilty of causing a child to engage in sexual activity by photographing herself and sending him pictures, and asking her to make an indecent video.
Gorman was remanded in custody for background reports and will be sentenced next month.
Sheriff Derek Livingston placed him on the sex offenders' register and said a prison sentence was "inevitable".
A man has been convicted of paying a 13-year-old school girl to send him sexually-explicit photos of herself.