Analytic dispersion relation is derived for resistive wall modes (RWMs) in rotating plasmas, which gives the growth rate and the real frequency. The given parameters are wall information (radius, thickness and volume resistivity) and equilibrium quantities at a plasma surface and at a singular point of the generalized Newcomb equation, which is an inertia-less linearized ideal magnetohydrodynamic equation with equilibrium rotation. Derivation of the dispersion relation is based on the generalized matching theory proposed by the present authors, which exploits the inner 'region' with finite width. It is found that the RWM stability is strongly affected by rotation shear, not at the rational surface, but at the singular point of the generalized Newcomb equation.