We have measured the Hall conductivity (${sigma}_{xy}$) of c-axis-oriented $MgB_2$ thin films as functions of temperatures and magnetic fields. We found that the Hall conductivity (${sigma}_{xy}$) is expressed by the sum of two terms, ${sigma}_{xy}=C_l/H+C_3H$, where the coefficient $C_1;and;C_3$ are independent of the magnetic fields and have positive values. The coefficient $C_1$ is strongly dependent on the temperature, while the $C_3$ is weakly dependent on the temperature. We have obtained that the $C_1$ is proportional to $(1- T/T_c)^n$ with n = 4.2, which is consistent with the data observed in $La_{2-x}Sr_xCuO_4$ superconductors with low anisotropy ratio.