Rodriguez was involved in an altercation with Brighton defender Gaetan Bong in the second half of West Brom's 2-0 victory on January 13.
Bong made a complaint against Rodriguez after the forward appeared to squeeze his nose and waft a hand at the Cameroon international.
And the FA has now confirmed Rodriguez has been charged following an assessment of the incident.
"It is alleged he used abusive and/or insulting words which included a reference to ethnic origin and/or colour and/or race," said the FA statement.
"Rodriguez has until 16 February 2018 to respond to the charge."
Speaking after the incident, Bong alleged Rodriguez had used "racist comments".
Referring to Rodriguez's gesture, Bong told SFR Sport: "He did that because of the colour of my skin. Everybody can see this gesture. And I asked him to repeat what he said.
"At this moment, I think he realised what he said. And he tried to limit the damage."
In a statement released following the FA charge, West Brom's director of football administration Richard Garlick defended Rodriguez.
"As a club we remain fully supportive and committed to backing Jay throughout this process," Garlick said.