Drift waves in a rotating toroidal plasma are considered for an axisymmetric, large aspect-ratio tokamak with concentric, circular magnetic surfaces. The analysis performed is based on rigorously derived eigenmode equations, coupled in poloidal mode numbers through the toroidal effects. Plasma rotation is driven by the radial electrostatic field typical for the H confinement mode of plasma in tokamaks. The strong and weak coupling approximation that takes into account the toroidal coupling of normal modes centered on the neighbouring rational surfaces are considered. The derived eigenmode equation of the Weber type has two classes of solutions giving either marginally stable global drift modes or propagating drift waves which experiences shear damping Analytical dispersion relations for both global and propagating drift waves are obtained and their simple solutions are found for some limiting cases.