If a foreign born Civil War Soldier completed his term of service (and then some) would he be given American Citizenship?

I have an ancestor that was born in Lier, Buskerud, Norway on October 9, 1837 and immigrated to American in the summer of 1853. On September 27, 1861 he enlisted into the Army, at San Francisco, and was mustered in the same day to the 2nd CA Cav, Co. K. He completed the required three year term and re-enlisted September 3, 1864 and promoted to Corporal, the following day. He mustered on September 16, 1864 and transferred to Co. M on October 22, 1864. He mustered out on July 22, 1866 at Camp Douglas, Utah Territory. Would he have been granted citizenship during or at the competition of his term of service?  And if so, how would I prove this? Are there specific records to explore?

Luci Baker Johnson

P.S. I have a copy of his 47 page Compiled Service Record and am working towards getting his pension record. He lived in Helena, MT until his death, April 1896.