The creature wandered onto the tarmac within the airport boundary on Friday afternoon.
Its appearance was caught on photographer Andrew Easby's live webcam stream.
Airport security staff were dispatched in a vehicle to try and locate the animal, which posed a hazard to incoming aircraft.
However it had already left the area by the time they arrived.
No flights arrived or departed while the deer was on the runway.
The webcam also captured the Friday arrival of a private plane chartered by Leeds Rhinos to take the squad to France.
The ASL Airlines aircraft touched down heavily before picking up the team, who flew to Perpignan to face Catalans Dragons. They fell to a 26-22 defeat.