EXCLUSIVE

Rapper Young Jeezy was arrested in Atlanta for battery, false imprisonment, and making terroristic threats against his own son ... TMZ has learned.

According to the charging documents -- obtained by TMZ -- Jeezy got into a fight with his son in a bathroom and he threw his son into the glass shower door, causing the son to hit his head. Then Jeezy allegedly punched him in the face, dragged him into the bedroom, threw him on the bed and pummeled him.

According to the incident report, Jeezy's son attempted to escape but the rapper's bodyguard blocked the stairwell.

The docs go on -- claiming Jeezy subsequently choked his son and said, "I will kill you." According to police docs, Jeezy's son claims his dad said, "I will put a bullet in your head right now," adding, "If I could get away with it, I would kill you." The incident allegedly occurred in Sept., 2012.

We've learned Jeezy turned himself in to authorities Friday after a grand jury warrant for each charge was issued. He bonded out soon after for $45,000.