The Frenchman could face a minimum five-game ban for his goal celebration, which is alleged to be an anti-Semitic gesture created by comedian Dieudonne M'bala M'bala.
A statement from the Baggies read: "West Bromwich Albion has noted The FA's charge against Nicolas Anelka regarding the gesture he made after scoring his first goal against West Ham United on December 28.
"Anelka has received a 34-page document explaining the allegations against him and informing him that he has until 6pm on Thursday to respond. The player is now considering his options.
"Under FA rules, Anelka remains available for first-team selection until The FA's disciplinary process has reached its conclusion. Following this, the Club will conclude its own internal enquiry."
As a result of the gesture, West Brom's sponsors Zoopla have decided not to renew their deal with the club at the end of the season.