Applying tensile stresses on straight soft magnetic ribbons before core fabrication is a routine method of inducing magnetic anisotropy, while methods of stress annealing of ribbons after core winding are seldom explored. In this study, we utilize a novel approach to induce magnetic anisotropy by applying radial stresses on tape-wound cores of Fe73.5Si13.5B9Cu3Nb1 (at. %) ribbon during crystallization heat treatment. The results show that while stress annealing does not change the structural characteristics of annealed samples, the magnetic anisotropies induced can increase to values ~3−5 times larger than the sample annealed in the absence of external stress. This increase in magnetic anisotropy energy is associated with ~25−50% decrease of magnetic inductance in the treated cores. These results suggest that the magnetic properties of nanocrystalline soft magnetic alloys can be effectively tuned by applying radial stresses.