The man was arrested after a video was posted online by vigilante group Wolf Pack Hunters UK.
The sting at a Tesco store was captured on Facebook and broadcast live to thousands of viewers on Saturday morning.
The group’s members pose as young girls on social media and then confront men they claim have arranged to meet them for sex.
Information is then passed to the police.
Police have confirmed officers were called to the Tesco store in Gavin’s Mill Road, Milngavie, at around 10.20am on Saturday and that a 47-year-old man was later taken into custody.
He has since been charged in connection with alleged indecent online communications.
However, a police spokesman said: “If you think someone may be abusing children, please contact the police rather than taking the law into your own hands.
“Police Scotland is fully committed to the investigation of child abuse using all of its resources, nationally and locally, to protect Scotland’s children.
“If you are concerned that children may be at risk or suspect someone may be abusing children then please call 999 if you think there is immediate threat, or 101.”
The spokesman continued: “The Sex Offender Community Disclosure scheme is another way members of the public can raise concerns about an individual in a child’s life and application can ultimately lead to a disclosure to the parent or carer.
“Application to this scheme is through the Police Scotland website, where details are available of how to apply online.”