John Bowlen -- son of Broncos owner Pat Bowlen -- has cut a plea deal in his DUI case ... the one where he told a cop, "So you know who my father is?"
As we previously reported, the 31-year-old -- who used to work for the Broncos -- was busted in July 2017 when cops say he was blazing down a California highway around 100mph while drunk.
And to make matters worse ... he had a puppy in the backseat.
Now, we've learned ... John appeared in a San Luis Obispo court Thursday and plead no contest to driving under the influence.