The optical properties of the (Ga2O3)(n) clusters, with n = 1-10, have been studied within the framework of time dependent density functional theory. The gallium oxide cluster geometries showed evolution from planar configuration (C-2v) for Ga2O3 to layered globular configuration (C-2v) for (Ga2O3)(10) via corundum configuration (D-3d) for (Ga2O3)4. For n <= 5, with the increase in coordination of Ga and O atoms, the polarizability decreases with the size of the cluster. For n >= 6, with the stabilization of average coordination number for gallium and oxygen atoms, the decrease in polarizability is very small. Further, the optical absorption spectra and the corresponding optical gap have been calculated. The overall shape of the calculated spectra strongly depend on cluster geometries. With the increase in size, the discrete spectra of small clusters evolves into quasicontinuous spectra. For n = 10, the spectra show a smooth absorption edge that is a characteristic of the bulk. It is observed that the optical gap oscillate with an increase in the cluster size. The calculated optical gap of these clusters are lower than the band gap of alpha- and eta-Ga2O3 phases. The underestimation of the calculated values of the cluster optical gap is due to the use of local density approximation.