This paper presents a design methodology and a realization of a circularly polarized (CP) antenna for FMCW radar at mm-wave frequencies on-chip, which combines antennas of different resonance frequencies to increase the operation bandwidth and allow for high resolution radar. The antenna consists of four dipoles with an on-chip ground plane operating at two resonance frequencies combined with a matching and feeding network, which enables both a frequency selectivity in advantage for the resonant antenna and radiation of circular polarization. The dipole arms are based on shorted λ/4 resonators, which are enhanced with series capacitances for increased radiation efficiency. A method for the broadband characterization of CP antennas and the measurement results of the designed CP antenna are presented. It is shown that the antenna covers a bandwidth between 220 GHz and 260 GHz, indicating the feasibility of both the measurement method and the antenna concept.