The 24-year-old is due at Furness Magistrates' Couty next Thursday to answer a Section 20 charge of GBH without intent. The maximum sentence is a five-year imprisonment.
Rigg made an official complaint last week, after the incident left him with two breaks in his jaw.
Cotterill had already been charged with violent conduct by the Football Association, and is suspended from all football matches while the FA carries out its disciplinary procedures.