We study both experimentally and theoretically the propagation of light in the fs-laser written rotating square waveguide arrays and present the first experimental evidence of light localization induced by the rotation of periodic structure in the direction of light propagation. Such linear light localization occurs either in the corners of truncated square array, where it results from the interplay between the centrifugal effect and total internal reflection at the borders of truncated array, or in the center of array, where rotation creates effective attractive optical potential. The degree of localization of linear bulk and corner modes emerging due to the rotation increases with the increase of rotation frequency. Consequently, corner and bulk solitons in rotating waveguide arrays become thresholdless for sufficiently large rotation frequencies, in contrast to solitons in nonrotating arrays that exist only above the power threshold. Focusing nonlinearity enhances the localization degree of corner modes, but surprisingly initially it leads to broadening of bulk nonlinear states, followed by their relocalization at high input powers. Our results open new prospects for control of evolution of nonlinear multidimensional excitations by dynamically varying potentials.