Busch will apparently play himself in an upcoming episode that sees him seeking counselling from Dr Charlie Goodson (Sheen).
The controversial race car driver booked the guest appearance mainly because he is a "giant Charlie Sheen fan", a source told TMZ.
Anger Management's second season also features celebrity cameos by former Voice coach Cee Lo Green and Lindsay Lohan.
The sitcom is loosely based on the 2003 film of the same name and centres on an eccentric therapist who helps high-profile clients deal with anger issues.
FX airs Anger Management on Thursdays at 9.30 ET.
Watch a preview of season two below: