Unfortunately no way I know of. It seems to prefer hanging around the middle field and doesn't venture to the sides, though if given the chance it will follow you onto the dock.
I managed to win by essentially running in circles around the farm and using all four keys so I could slip through to the opposite side. If you manage to 'aggro' the deer, it does settle after a certain amount of time. I don't know exactly how long it takes, unfortunately.
You can throw it off by being inside and stepping close to the door, just enough to open the door. The deer will become aggressive, but it will run off in some other direction because you're inside.