We propose and numerically design a magnetically tuned orbital angular momentum (OAM) generator operating in the terahertz (THz) regime based on air-clad microstructured optical fibers (ACMOFs) infiltrated with functionalized liquid crystals (LCs). The ACMOFs consist of a ring-like air hole layer uniformly arranged the outer surface, serving as both the whispering gallery mode (WGM) microcavity and angular grating. Numerical simulations indicate that due to the periodic refractive index modulation in azimuthal direction through filling LCs by every other air hole, WGMs would be coupled into specific OAMs, whose operation frequency and topological charges could be tuned by adjusting the refractive index of LCs that through applying external magnetic field. The proposed magnetically tunable ACMOF-based THz OAM generator possesses several desirable merits such as compatibility with functional materials, ease of integration, and flexible structure, which is anticipated to find potential applications in future OAM-based THz communication systems.