We show that truncated rotating square waveguide arrays support new types of localized modes that exist even in the linear case, in complete contrast to localized excitations in nonrotating arrays requiring nonlinearity for their exist- ence and forming above the energy flow threshold. These new modes appear either around an array center, since the rotation leads to the emergence of the effective attractive potential with a minimum at the rotation axis, or in the array corners, in which case localization occurs due to competition between the centrifugal force and total internal reflection at the interface of the truncated array. The degree of localization of the central and corner modes mediated by the rotation increases with the rotation frequency. The stable rotating soliton families bifurcating from linear modes are analyzed in both focusing and defocusing media.