Magnetic alignment technology using the modulated rotating magnetic fields (MRF) enables formation of tri-axial grain arrangement of the substances with tri-axial magnetic anisotropy. In this review, we introduce a high potential of magnetic alignment technique as the fabrication process of tri-axially grain-oriented cuprate superconductors. As the first topic, we reported the tri-axial magnetic alignment of rare-earth-based and bismuth-based cuprate superconductors operated at room temperature. In the second topic, we show the importance of single-ion magnetic anisotropy of the rare-earth ions as a determination factor of magnetization axes and the tri-axial magnetic anisotropy in rare-earth-based cuprate superconductors. The final topic is the fabrication of tri-axially grain-aligned ErBa2Cu4O8 (Er124) ceramics under a modified MRF. To date, the Er124 ceramic with the degree of in-plane orientation with ~11 degree has been successfully fabricated by controlling the viscosity of slurry and introducing the oscillation type of MRF.