Robert Ferguson, 60, was on trial at Carlisle Crown Court, where he denied a charge of causing or inciting a child aged under 13 to engage in sexual activity on a date before June 19, 2015.
But a jury found him guilty on a majority verdict.
Jurors heard that the girl had informed police that Ferguson had asked her to keep his criminal conduct “secret”.
Judge Peter Hughes QC adjourned sentence to June 20 and remanded Ferguson, of Warwick Road, Carlisle, in custody.
Judge Hughes told him: “In these circumstances the sentence that I pass upon you must be a custodial one.
"I take the view it is better you start to serve that sentence from today.”
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