Terpfan is right... it is a US Army uniform "general service" button ("general service" meaning it was worn by all branches of the army except the Engineer Corps). More specifically, the version you found has a raised rim encircling the emblem, which dates it to being from 1910 onward to the present. I should mention, from the World War One era to 1923, those buttons had a "black finish" applied to their brass front, as a sort of camouflage. If you can clean yours a bit better, see if it has any of that "black finish" on its front.
Looks like there's no hope of discerning your button's backmark, so that time-dating clue is unavailable.