The incident occurred during the second half of the Potters’ 1-0 win over Arsenal on Sunday, and was not seen at the time by referee Mike Jones or his officials.
However, the FA has stepped in after reviewing video footage, and has decided to charge the Scottish midfielder.
Stoke have been left furious with the decision, and have vowed to fight the FA charge.
The club issued a statement which read:
“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.”
Relations between Stoke City and Arsenal have been strained since 2010, when Stoke captain Ryan Shawcross broke the leg of Gunners midfielder Aaron Ramsey with a horrible tackle.