We experimentally study the effects of inner cylinder rotation on the displacement flow of two Newtonian fluids along a horizontal eccentric annulus, with differing viscosities and densities. With the rotation of the inner cylinder, the flow behavior changes from stratified to helical, as rotation dominates buoyancy, or directly to an azimuthally dispersive regime when rotational velocity dominates axial velocity. Flow separation is observed to occur when eccentricity is high: the displacing fluid is contained in the wide gap of the annulus, and the effective displacement is delayed. Rotation is effective in creating azimuthal flow in the narrow gap, where there is limited flow and bottom-side residual fluid may be present. In most cases, rotation improves the displacement (volumetric efficiency) by shortening the length of the axial elongation of the displacement front, and eventually, steady displacements are seen. The study is motivated by displacement flows occurring during the primary cementing of long horizontal oil and gas wells. Rotating the inner cylinder (casing) is recommended. Our results suggest that this practice increases azimuthal dispersion and can prevent a narrow mud channel from forming if the excess fluid volume is used.