An analytical solution of electromagnetic fields in homogeneous plasma anisotropic media is obtained in this paper. In the source-free plasma anisotropic media, the source-free Maxwell's equations are utilized, where the expansion of plane wave factors is made in terms of the spherical vector wave functions in isotropic media, and the Fourier transformation is then applied. As a result, the field expressions represented using eigenfunctions are obtained in spectral domain. Applying boundary conditions on the spherical interface between air and plasma anisotropy, the electromagnetic fields of the plane wave scattered by a plasma anisotropic sphere are derived. Numerical results for the very general plasma dielectric material media are obtained, and those in a special case are compared between the present method and the Method of Moments (MoM) speeded up with the Conjugate-Gradient Fast-Fourier-Transform (CG-FFT) approach. The formulations in this paper can be generalized to those of more complex cases, such as layered plasma anisotropic sphere, plasma sheath, as well as plasma anisotropic material coated conducting sphere.