Jameis Winston -- Late Night Chicken Run ... Hits Roscoe's with 3 Women

Jameis Winston and Barack Obama have something in common -- they both ordered the same exact meal at Roscoe's House Of Chicken 'N Waffles.

TMZ Sports has learned the Florida State QB hit up the iconic L.A. chicken joint around 12:30 AM Sunday for a late night meal.

Our poultry sources tell us ... Winston was dressed in his FSU warm-ups and arrived with 3 women in tow.

We're told Winston ordered the "Obama Special" ... 3 wings and a waffle ... which was named after the President when he ordered the meal during a visit back in 2012.

The good news? Seems like Jameis listened to Kevin Hart's advice ... 'cause we're told he paid for the meal without incident.

Baby steps ...