The unique gate-voltage dependent optical properties of graphene make it a promising electrically-tunable plasmonic material. In this work, we proposed in situ control of the polarization of nanoantennas by combining plasmonic structures with an electrostatically tunable graphene monolayer. The tunable polarizer is designed based on an asymmetric cross nanoantenna comprising two orthogonal metallic dipoles sharing the same feed gap. Graphene monolayer is deposited on a Si/SiO2 substrate, and inserted beneath the nanoantenna. Our modelling demonstrates that as the chemical potential is incremented up to 1 eV by electrostatic doping, resonant wavelength for the longer graphene-loaded dipole is blue shifted for 500 nm (~10% of the resonance) in the mid-infrared range, whereas the shorter dipole experiences much smaller influences due to the unique wavelength-dependent optical properties of graphene. In this way, the relative field amplitude and phase between the two dipole nanoantennas are electrically adjusted, and the polarization state of the reflected wave can be electrically tuned from the circular into near-linear states with the axial ratio changing over 8 dB. Our study thus confirms the strong light-graphene interaction with metallic nanostructures, and illuminates promises for high-speed electrically controllable optoelectronic devices.