This paper describes the enhanced performance of the microcrystalline silicon (µc-Si) thin-film solar cells due to the incorporation of plasmonic nanostructures. Finite-difference time-domain numerical modeling is used to calculate the optical properties of the solar cells such as the absorption and the short-circuit current density (J_sc). In this paper, two-dimensional(2D) periodic arrays of various geometries of plasmonic nanostructures such as nano-rings, nano-discs, nano-hemispheres, and nano-cubes are employed on the back side of the solar cells to increase the absorption for the longer wavelengths of the incident light, where most of the photons remain unharvested due to extremely low absorption coefficients of µc-Si material. These plasmonic nanostructures are compared in terms of solar cell performance, and it is found that the 2D periodic arrays of nano-rings show significant absorption enhancement at multiple wavelengths, thereby leading to a substantial enhancement in the J_sc. An enhancement of 35% in the J_sc is obtained when a 2D periodic array of plasmonic nano-rings is present on the back side of the solar cell, which is higher than that of the µc-Si solar cells having arrays of plasmonic nanostructures of other geometries (i.e., nano-discs, nano-cubes, nano-hemispheres). It is observed that the enhancement in the absorption is attributed to the enhanced electromagnetic fields in the active layer due to several localized surface plasmon modes that are excited in the plasmonic nanostructures at different wavelengths. Moreover, the effect of the thickness of the spacer layer (the layer between the metal back-reflector and plasmonic nanostructure arrays) on the performance of different plasmonic solar cells is examined.