We demonstrate optical control of the polarization eigenstates of a neutral quantum dot exciton without any external fields. By varying the excitation power of a circularly polarized laser in microphotoluminescence experiments on individual InGaAs quantum dots we control the magnitude and direction of an effective internal magnetic field created via optical pumping of nuclear spins. The adjustable nuclear magnetic field allows us to tune the linear and circular polarization degree of the neutral exciton emission. The quantum dot can thus act as a tunable light polarization converter.