US Military collar insignia discs have several identifying characteristics:
1- They show a soldier's branch of service or unit -- never his rank (such as Corporal or Captain or Major, etc)... but this disc says "CAPT".
2- Their diameter is specified to be exactly 1-inch... but this disc appears to be approximately 7/8-inch.
3- Their "background" is always dots arranged in diagonal rows, or cross-hatching, or plain -- but this disc's background looks like tiny wavelets or a cobblestoned street.
Dating Metallic Insignia: Collar Disks
So, this disc seems to not be a US Military collar-disc insignia.
It is known that the Police and Fire Department services have had collar-disc insignia. See some of the varieties at lower right on this webpage:
EMS Collar Insignia -
However, for many decades, Police and Fire Department
rank insignia have tended to be the same as US Army rank insignia. (Chevrons for non-officers, and bars or an oak-leaf etc for officers.) Still, this disc
might be an early-1900s Police or Fire Department rank insignia.