The effect of neutron spin rotation at Laue diffraction in a weakly deformed neutron-transparent
noncentrosymmetric crystal has been described theoretically and studied experimentally. The effect is due to the bending of a Kato trajectory of the neutron in the deformed crystal. At a certain type of the deformation, one of two neutron waves excited at Laue diffraction, which propagate in opposite crystal fields in the crystal with no center of symmetry, leaves the crystal. As a result, the spin of the remaining neutron wave will rotate by a certain angle with respect to initial direction due to the interaction of the magnetic moment of a moving neutron with the intracrystalline electric field. This effect is absent in an undeformed perfect crystal, where only the depolarization of a beam occurs because both waves in opposite electric fields have the same amplitude. The method of controlled deforming of a perfect single crystal by creating a temperature gradient in it is developed. Thus, a new way for measuring electric fields acting on neutrons in non-centrosymmetric crystals is implemented, as well as a method for controlling these fields in experiments to study the fundamental properties of the neutron.