A rotating particle in electrorheological (ER) fluid leads to a displacement of its polarization charges on the surface which relax towards the external applied field E0, resulting in a steadystate polarization at an angle with respect to E0. This dynamic effect has shown to affect the ER fluids properties dramatically. In this paper, we develop a dynamic effective medium theory (EMT) for a system containing rotating particles of finite volume fraction. This is a generalization of established EMT to account for the interactions between many rotating particles. While the theory is valid for three dimensions, the results in a special two dimensional configuration show that the system exhibits an off-diagonal polarization response, in addition to a diagonal polarization response, which resembles the classic Hall effect. The diagonal response monotonically decreases with an increasing rotational speed, whereas the off-diagonal response exhibits a maximum at a reduced rotational angular velocity ω0 comparing to the case of isolated rotating particles. This implies a way of measurement on the interacting relaxation time. The dependencies of the diagonal and off-diagonal responses on various factors, such as ω0, the volume fraction, and the dielectric contrast, are discussed.