Police in Sugar Land, Texas say Adrian Peterson fessed up to throwing back shots of a vodka mix at a poker game early Sunday morning ... just hours before he was arrested for DWI.

The officer alleged in the docs he encountered Peterson asleep at the wheel of a running black Mercedes SUV that was next to some pumps ... and he claimed once he woke up the unconscious ex-Minnesota Vikings star,

Former NFL running back Adrian Peterson was caught sleeping at the wheel of a running car before his arrest this week.