Adam appeared to stand on the Frenchman's leg during the second half of Stoke's 1-0 victory over the Gunners at the Britannia Stadium on Saturday.
The incident was not seen at the time by referee Mike Jones and his fellow match officials but it was caught on TV cameras and referred to a three-man panel of former elite referees to review.
"Charlie Adam has today been charged by The FA for violent conduct, following an incident with Arsenal's Olivier Giroud," said the FA in a statement.
"For an FA charge to follow, all three panel members must agree it is a sending-off offence. In this instance, the panel were of the unanimous decision that it was an act of violent conduct."
Adam has until 6pm on Tuesday to respond to the charge but the Potters have already issued a statement saying they plan to fight verdict.
"The Club have learnt within the last hour that The FA have chosen to charge Charlie Adam following an incident involving Olivier Giroud in Saturday's Barclays Premier League game against Arsenal.
"Charlie and the Club are surprised and disappointed to learn of this and will appeal vigorously against the decision."