Philip McGinn, 42, from Liverpool, was found with an injured leg and had to be rescued with a gamekeeper's 4X4 after getting stuck in a fence.
He was banned from driving for 18 months after admitting escaping from a police car and drink driving.
He also admitted failing to provide a roadside breath test.
The court heard the use of the helicopter cost £1,300.
A dog handler was also called in after McGinn escaped on the A5 at Llidiart y Park near Corwen on 16 August.
Judge Niclas Parry said he had been "utterly foolish" and ordered him to pay £400 towards the cost of calling out the helicopter and £200 prosecution costs.
"You caused great inconvenience to public services," he said.
He also gave McGinn a 12-month community order during which he must carry out 120 hours of unpaid work.
A police helicopter was called out after a drink driver fled and ran off into the Denbighshire countryside, Mold Crown Court has heard.