This is a small brass button about the size of a dime. It has an eagle on the front with its head to the left and a shield on its body. It has branches in its feet and 13 stars above its head. Back of button is missing.
US Army "Great Seal" button, with a raised border encircling it, dates from about 1911 through the present (still in use today). No back means no backmark, so yours cannot be dated any more narrowly than the above information... except to say that with the back having been corroded out of it, it's probably over 50 years old.
I don't mean to be a party pooper but your button could also be a civilian fashion one. The lack of a back and the look of the globe over the eagle's head make me think that.
Could you post a clearer image?