Florida State Football -- RB Investigated for Punching Woman ... Allegedly

More alleged man vs. woman violence surrounding the Florida State football team -- this time, the starting running back is under investigation for allegedly punching a 21-year female in the face.

Officials say cops are investigating 19-year-old Dalvin Cook over a June 23 incident -- in which a woman was attacked outside of a Tallahassee bar.

Cops say the alleged victim was drunk -- and only suffered minor cuts and bruises -- but was able to I.D. Cook as her assailant. She plans to press charges.

The woman told ESPN Cook became enraged when he asked for her phone number and she shot him down. During the altercation, Cook's group allegedly told the woman they were football players and they could "buy her" in two years.

State Attorney Willie Meggs says Cook has not been charged with a crime so far ... but plans to issue a warrant for Cook's arrest on suspicion of misdemeanor battery.

Meggs has his hands full with FSU football players -- including ex-QB De'Andre Johnson who punched a woman in the face at a bar ... after she struck him in the face first.