In this work, the electromagnetic scattering in general rotationally symmetric inhomogeneous anisotropic spheres is investigated. A rigorous full-wave solution is presented based on the volume integral equation. The solution is achieved by expanding the unknown fields in fully orthogonal Dini-type spherical vector wave functions. This formulation allows the study of general rotationally symmetric gyrotropic spheres with varying permittivity and permeability tensors. We investigate the validity of the developed method, which is next applied on the computation of the scattering cross sections of inhomogeneous rotationally symmetric gyroelectric and gyromagnetic spheres.