Adrian Peterson -- SHOTS ON ME ... Buys Vodka for Entire Texas Bar!

He may not be a Cowboy (yet) ... but they sure as hell loved Adrian Peterson in Texas this weekend ... when the guy walked into a bar ... and bought EVERYONE a shot of vodka!

It all went down at the Flying Pug Bar in Houston on Sunday night ... where sources tell TMZ Sports the running back was the life of the party from the moment he walked in the door.

We're told AP enjoyed some whiskey ... but wanted to make sure everyone else got their drank on too -- so he ponied up for a round Grey Goose on him.

The fun didn't stop there ... 'cause Peterson's group moved the party down the street to another bar called Exit 73 ... and continued to rage!

The best part of the story ... Peterson played it SAFE at the end of the night and let a sober pal drive him home.

Even bald guys gotta let their hair down every now and then.