Cole caused outrage during the 1-1 draw at Wembley when he tweeted: "Immigration has surrounded the Wembley premises! I knew it was a trap! Hahahaha. The only way to get out safely is to wear an England jersey and paint your face w/ the St. George's flag!"
Cole later withdrew the comments, but was still charged by the FA.
The former Chelsea player accepted the charge on Thursday and is now likely to receive a fine or a warning.
An FA statement read: "The FA has charged West Ham United's Carlton Cole with improper conduct relating to media comments. The charge relates to comments made on Twitter during the England v Ghana fixture on 29 March 2011."
Cole, who has scored 11 goals for the Hammers this season, has requested a personal hearing which will take place before April 21.
It is not expected that the 27-year-old will be banned for any of West Ham's remaining matches because of the comments.
A similar case in January saw Ryan Babel receive a £10,000 fine for posting a mocked-up picture of referee Howard Webb wearing a Manchester United shirt on Twitter following Liverpool's 1-0 defeat at Old Trafford in January.