Duggap is right. More specifically, it is the 1854-through-1874 version of US Army "general service" button for Enlisted-men's ranks (private, corporal, sergeant).
The vast majority of the 1854-1874 version were manufactured between 1854 and 1865. Because there were so many "leftovers" at the end of the civil war, very few needed to be made until 1875, when the emblem for "general service" buttons was changed to have a highly-raised shield on the eagle's chest. In the photo below, yours is at right, and the 1875-1902 version (having a highly-raised shield) is in the middle.