Demetri,
Closest serial # to your 21275 that I found in my SRS research books is serial # 21252, next serial # listed is 21692 - both of these Spencer Carbines were issued to Company D, 5th New York Volunteer Cavalry on April 22, 1864. Hard to say if your Spencer (carbine or rifle??) went to this same unit because of the gap in serial #s listed.
On the other hand, your Spencer may have been included as part of a state purchase of Spencer firearms and were sent to a different unit, in that case those serial #s were never recorded or appear on any list.
Without seeing any photos and speculating on your Spencer, it may have been modified after the Civil War and made into a single shot shooter, especially if the stock has been completely replaced. Just speculating, though, still want to see your photos.
I have a thread/post on SSS on HOW TO TAKE GREAT PHOTOS of your Spencer. Just try to use daylight and not artificial lighting to photograph your Spencer.
Two Flints