Jerry Sandusky's Son Jon -- THE DUI MUG SHOT

TMZ has obtained the mug shot for Jerry Sandusky's son Jon Sandusky -- taken moments after the Cleveland Browns director of player personnel was arrested for DUI yesterday.

36-year-old Jon was initially pulled over in Fargo, ND early Tuesday morning after cops say he made an illegal turn. During the stop, cops suspected he was hammered and tried to administer a breathalyzer test ... but Jon refused.

Instead, cops ordered Jon to do field sobriety tests -- and he clearly didn't perform well enough, 'cause he was immediately arrested for driving under the influence.

Sandusky was hauled to a nearby station where he was booked -- posed for his mug shot -- and was eventually released.

It's been a rough couple of years for the Sandusky family -- Jon's sick pedophile father Jerry was arrested in 2011 for raping a bunch of boys in the Penn State locker room.

He's currently rotting in prison ... where he will most likely die.