α-Ga2O3 has garnered significant attention as a promising next-generation material for applications in power-switching and deep ultraviolet optoelectronics owing to its ultrawide bandgap. However, fabricating α-Ga2O3-based devices with a vertical structure is challenging because α-Ga2O3 requires heteroepitaxial growth on a heterogeneous substrate, typically insulating sapphire. In this study, we investigated the heteroepitaxial growth of a-, m-, and r-plane α-Ga2O3 on rhombohedral indium tin oxide (rh-ITO) electrodes via mist chemical vapor deposition. X-ray diffraction (XRD) 2θ-ω and φ scan analyses revealed that a-, m-, and r-plane α-Ga2O3 epitaxial thin films were successfully grown on rh-ITO bottom electrodes when α-Fe2O3 buffer layers were inserted. No phase separation or in-plane rotation was observed in the XRD results of the α-Ga2O3 thin films. The α-Fe2O3 buffer layers facilitated the preferential growth of α-Ga2O3 on various planes of rh-ITO. The surface morphology of the a-, m-, and r-plane α-Ga2O3, examined via field emission scanning electron microscopy, differed depending on the crystal plane. The results obtained in this study have potential applications in the development of vertical-structured devices with α-Ga2O3 thin films.