In situ small-angle X-ray scattering (SAXS) rheology is used to st;study the dynamic process of shear alignment in a lamellar poly(styrene-b-ethylene propylene) diblock copolymer, at temperatures far below the microphase separation transition temperature. We have focused on the alignment dynamics at time scales shorter than 1 cycle of deformation. To extract this valuable information, we use prealigned specimens and follow subtle changes in the orientation during a steady shear deformation. Two notable changes in the azimuthal SAXS intensity are observed: the maximum of the main peak induced during prealignment shifts to lower azimuthal angles and a secondary peak develops and shifts to higher angles. : We effectively modeled the shift of the main peak maximum by assuming that lamellae rotate with the;. vorticity component of shear. This provides conclusive evidence for lamellar rotation in block copolymers, as opposed to a discontinuous transformation such as lamellar dissolution and reformation. Lamellar rotation also supports our previously proposed mechanism for kink band formation.