We report on the first polarimetric plasmonic biosensor based on arrays of bowtie nanoantennas. Using the Finite Element Method (FEM) the phase retardation between the components of light polarized parallel and perpendicular to the axis of the nanoantennas is studied. After optimizing them for high volumetric sensitivity at a wavelength of 780 nm, sensitivities ~5 rad/RIU are obtained, corresponding to a detection limit ~10-7 RIU when using the polarimetric readout platform. Surface sensitivity values resulted from studies of phase retardation changes from a coverage of bioreceptors and analytes.