The English governing body have been investigating the gesture, which Anelka made during a goal celebration in the Baggies' 3-3 draw at Upton Park.
The salute, which was created by Anelka's friend and comedian Dieudonne M'bala M'bala, is alleged to have anti-Semitic connotations.
A statement from the FA said: "It is alleged that, in the 40th minute of the fixture, Anelka made a gesture which was abusive and/or indecent and/or insulting and/or improper, contrary to FA Rule E3.
"It is further alleged that this is an aggravated breach, as defined in FA Rule E3, in that it included a reference to ethnic origin and/or race and/or religion or belief."
The fallout of the incident has resulted in the club's sponsors Zoopla deciding against renewing their sponsorship deal at the end of the season.
The Frenchman, who faces a minimum of a five-match ban, has until 6pm on January 23 to respond to the charge.