Det Con Francois Olwage, 52, from Stevenage, Hertfordshire, spoke to the girl for two weeks on a chat forum.
But the girl was in fact an undercover police officer.
He was convicted of attempted sexual communication with a child and attempting to cause/incite a girl aged 13 to engage in sexual activity.
The counter-terrorism officer was also found guilty of attempting to meet a girl under the age of 16 following grooming.
Winchester Crown Court heard Olwage was having explicit sexual conversations with the “girl”, who had the username Smile Bear, before suggesting they meet in what the undercover officer had said was her hometown of Basingstoke, Hampshire.
Prosecutor Peter Shaw said the divorced father-of-three had taken the train to meet the girl on 28 October and was arrested after stopping at a Mcdonald’s.
On that day he was listed as “on duty working from home”, Mr Shaw said,
When officers searched his bag they found condoms, a bottle of lubricant and a packet of erectile dysfunction tablets, the jury heard.
Olwage told the court that he “never believed” Smile Bear was a 13-year-old girl and that he thought it was an adult “playing out a fantasy”.
At the start of the trial, he admitted an offence of improperly exercising his police powers and privileges in order to receive the “benefit of sexual gratification”.
The judge ordered the jury to find him not guilty of arranging/facilitating the commission of a child sex offence.
He has been remanded in custody and is due to be sentenced on 27 April.
