The 34-year-old performed the salute, putting one arm across his chest and straightening the other, during West Brom's 3-3 draw at West Ham United in the Premier League on 28 December 2013.
A statement published on Tuesday by the Football Association website reads "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 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.”
Anelka has until 1800 GMT on Thursday to respond to the charge.
If found guilty, he faces a minimum five-game suspension, under new anti-discrimination measures introduced by the FA in May last year.
The 'quenelle' was invented by French performer Dieudonné M'bala M'bala, better known as Dieudonné.
The gesture appears to be an inverted Nazi salute and Dieudonné been fined on previous occasions for anti-Semitic remarks.
Dieudonné says the gesture is anti-establishment and not anti-Semitic.
Anelka also declared after the 28 December match that the gesture is not anti-Semitic and he said he intended it as "a dedication" to Dieudonné.
The FA's decision to charge Anelka, after a three-and-a-half-week investigation, comes a day after West Brom's shirt sponsors, property website Zoopla, decided to end their association with the club.
British media reports suggested the company had called on West Brom to drop Anelka over the affair.
The former France international has continued to appear for the club despite the furore and played for 77 minutes in his side's 1-1 draw with Everton on Monday.