It is a US Army "general service" button for Enlisted-men's ranks (private, corporal, sergeant). The version you found was issued from 1875 to 1902. It is different from the earlier version (1854-74) of US Army "eagle button" in that the shield on the eagle's chest is very high-raised. Collectors of Military buttons call it the "chicken" eagle button, because that's what its eagle resembles in comparison to the eagle on the 1854-1874 version. Here's a photo which shows the difference between US Army Enlisted-men's buttons from 1854 to the present. The button on the left shows the 1902-to-present version, middle is your 1875-to-1902 "chicken-eagle" button, right is the 1854-1874 version.
(That helpful Educational photo was made and posted by our fellow What-Is-It forum ID-helper BigCypressHunter.)
