A$AP Rocky -- Charged with Assault ... Allegedly Slaps Female Fan

Rapper A$AP Rocky -- the guy behind the hit "F**kin' Problems" -- has been slapped with an assault charge in Philadelphia after allegedly getting all Rick James on a female fan this weekend ... TMZ has learned.

We know ... the alleged victim, a young mom, filed a criminal complaint with the District Attorney's Office today claiming she was attending the Made In America concert on Saturday when the rapper got violent.

The woman claims A$AP was trying to make his way through a crowd of dancing fans -- with a bunch of girls pulling on his shirt -- when A$AP turned and fired off an open-hand slap, connecting with her face.

The woman claims she was injured from the alleged slap -- suffering whiplash from the impact.

The D.A.'s office reviewed the case and has decided to charge A$AP with misdemeanor simple assault.

We reached out to A$AP's camp for comment -- so far, no word back.