In a short statement, the FA confirmed that Cole's tweet "was improper and/or brought the game into disrepute". He now has until 4pm on October 11 to respond to the charge.
Former Arsenal defender Cole posted the comment on Friday after his evidence in the racism trial of fellow footballer John Terry was questioned by the FA.
The FA had issued the written reasons for an independent commission finding Terry guilty of racially abusing Anton Ferdinand. The commission had also fined the ex-England captain £220,000 and banned him for four matches.
Terry's defence that he had not racially insulted the QPR defender was branded "improbable, implausible and contrived", but the commission also questioned Cole's statement in support of him.
In response to this, Cole tweeted: "Hahahahaa, well done #fa I lied did I, #BUNCHOFTW*TS."
He deleted the tweet soon after and issued an apology, which read: "I had just finished training and saw the captions on the TV screens in the treatment rooms about what was said in the FA Commission ruling about me.
"I was really upset and tweeted my feelings in the heat of the moment. I apologise unreservedly for my comment about the FA."
But Match of the Day pundit Alan Shearer said on the BBC One show on Saturday that Cole should be dropped for England's international match on Friday, rather than just fined by the FA.
"I think the FA can put a big statement out here by actually not fining him but actually banning him on Friday against San Marino. Because we've seen players fined £50,000, £60,000, £70,000. That's not a deterrent to them," he said.
"Stopping them from playing football will be a deterrent. If they do it quickly - which they haven't done in the case, which has taken 14 months - if they do it in four to five days, I think it puts a big statement out to the rest of the players."
Cole's FA charge follows a separate Twitter-related incident in which Rio Ferdinand was fined £45,000 by the FA for appearing to endorse a follower's use of the term "choc ice" in relation to Cole, referring to someone who is 'black on the outside, but white on the inside'.