The present cephalopod taxon was proposed by Smith (1938) as a variety of Orthoceras indianum Girty (1909, p. 47, pl. 6, figs. 13, 13a) from the Chesterian (Upper Mississippian; lower Carboniferous) Caney Shale in Oklahoma on the basis of similarities of gross conch shape and surface ornamentation. However, a phylogenetic relationship between these two taxa is uncertain because of the unknown internal morphologies of the Mississippian species. The transverse constrictions made by internal shell wall thickenings of this species warrant a placement in Bitaunioceras. The discovery from the Desmoinesian rocks represents the oldest and first Pennsylvanian record of this genus. Previous stratigraphic records of the genus range from the Sakmarian (lower Permian) of the southern Urals (Shimansky, 1954) and central Japan (Niko and Nishida, 1987) to the Guadalupian (middle Permian) of Sicily (Gemmellaro, 1890) and northern Mexico (Miller, 1944).

Bitaunioceras buckhornense was named by Niko et al. (2018). Its type specimen is Orthoceras bitauniense, a partial shell, and it is a 3D body fossil.