We develop a theory of the helicity driven nonlinear DC response of gated two-dimensional electron gas to the terahertz radiation. We demonstrate that the helicity-sensitive part of the response dramatically increases in the vicinity of the plasmonic resonances and oscillates with the phase shift between excitation signals on the source and drain. The resonance line shape is an asymmetric function of the frequency deviation from the resonance. In contrast, the helicity-insensitive part of the response is symmetrical. These properties yield significant advantage for using plasmonic detectors as helicity-sensitive terahertz and far infrared spectrometers and interferometers.