Twisting the wire will introduce both elastic and if twisted hard enough plastic deformation which is typically deterimental to the magnetic performance. Even small amounts of deformation will usually significantly change the magnetic properties, however in some cases such as iron the elastic stresses can increase the magnetic permeability due to the Reverse Villari effect. Plastic deformation always degrades the material.
Perhaps if the torsion of the material is too intense to the point of significantly altering the cross-section of the magnetic conductor such a magnetic permeability effect can be modified because the molecular alignment of the material would also be significantly altered.
Here is another paper describing magnetic changes in steel due to cold working. In this case formation of a ferritic magnetic phase in the austenitic phase.