A nonperturbative method for the evaluation of thermodynamic scaling functions in the critical region of three-dimensional anisotropic type-II superconductors is extended for the case of external magnetic fields with arbitrary angles with respect to the anisotropy axis. The calculations are carried out in the framework of the Ginzburg-Landau theory. Explicit relations are obtained for the angular dependence of the magnetization and specific heat. Our theoretical results are in good agreement with experiments performed in untwinned single crystals of YBa2Cu3O7–δ.