In the script for The Last Samurai Capt. Algren is mentioned as a veteran of the Indian Wars and a member of the US 7th Cavalry under the command of George Armstrong Custer. Though did he actually take part in the Battle of the Little bighorn? I do not recall this being mentioned.
The answer to that lies in the reunion between Gant and Algren. Gant was part of Custer's regiment and Algren assumed he had died, but Gant tells him that he refused to go.