I would guess somewhere between the Spanish American War and WWI when they started using white chevrons on the sleeves? It looks like the Eagle is facing forward, which changed somewhere between WWI and WWII (now facing backward as shown above in current).. Definitely after 1897 but before the end of WWI when the chevrons changed. the closest I can find is a 1917 (right at the start of WWI)- see plate #1 here:
http://www.quarterdeck.org/uniforms/1917/Plates%20Enlisted%2020-29.pdf