Stedman Bailey has officially been charged after cops say the former Rams wide receiver got caught knockin' boots at a Florida mall arcade.

TMZ Sports obtained the Broward County charging doc -- filed by prosecutors earlier this month -- where they formally accused Bailey of exposure of sexual organs, a first-degree misdemeanor.

The alleged incident went down July 27 at an arcade called Round1 inside the Pembroke Lakes Mall in Pembroke Pines, FL.

Prosecutors say Bailey, 35, “pulled down his clothing to engage and/or was actively engaging in contact of a sexual nature” in public at the bowling alley and arcade bar.

We reported on the crazy alleged incident earlier this summer.

Bailey, who played three seasons in the NFL before his career was tragically cut short when he was shot in the head in 2015, was arrested with a woman named Karina Manderson shortly after midnight on July 27 after they were allegedly caught having sex at the bar.

Stedman, according to cops, admitted he had his pants down, but swore they didn't have sex. He says he's fighting the charge.

If convicted, Bailey could face up to a year in county jail and a $1k fine.