A nonperturbative method for evaluation of thermodynamic scaling functions in the critical region of type-II superconductors, appropriate for high-temperature superconductors, is extended for the case of external magnetic fields with arbitrary angles with respect to the $c$ axis for the case of three-dimensional anisotropic superconductors. An explicit scaling function for the magnetization is presented, discussed, and compared with experimental data from measurements with applied fields along the $\mathrm{ab}$ planes.