It is known that critical fluctuations can change the effective anisotropy of a cubic ferromagnet near the Curie point. If the crystal undergoes a phase transition into the orthorhombic phase and the initial anisotropy is not too strong, then the effective anisotropy acquires the universal value A∗ = v∗/u∗ at Tc, where u∗ and v∗ are the coordinates of the cubic fixed point of the renormalization group equations in the scaling equation of state and expressions for nonlinear susceptibilities. Using the pseudo-epsilon-expansion method, we find the numerical value of the anisotropy parameter A at the critical point. Pad´e resummation of the six-loop pseudo-epsilon-expansions for u∗, v∗, and A∗ leads to the estimate A∗ =0 .13 ± 0.01, giving evidence that observation of anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is entirely possible.