The Katana first appeared in Season 3 Part 2 when Noshiko Yukimura used it to kill the Nogitsune the first time, and was given to Kira to kill the Nogitsune for the second time.
Stiles and Malia found the katana buried with Rhys's body in a wall in Eichen House. Noshiko used the sword to kill the nogitsune. It exorcised the spirit, which shattered the blade. Noshiko was not able to reforge it because she is not a thunder kitsune, so Kira has to fix it for her.