We obtain vector wave function expansion coefficients of the circularly-symmetric vector Bessel vortex beam based on the expansion of electromagnetic field in terms of vector wave function and the transformation of vector wave functions in different coordinate systems. Then, we obtain the expansion coefficients of reflection field, transmission field, and internal field of homogeneous uniaxial anisotropic media, which is illuminated by a circularly-symmetric vector Bessel vortex beam in any direction under the electromagnetic field boundary conditions. At last, we simulate the electric field distributions of reflection field, transmission field, and internal field in the cross sections and the total electric field distribution in xOz plane. The simulated results show that for a circularly-symmetric Bessel vortex beam incidence to uniaxial anisotropic media, the reflection field contour keeps a concentric ring structure, whereas the reflection field intensity distribution is asymmetric; there are two refracted rays in the transmission field, which brings about the distortion of the electric field intensity contour.