We present an electrically tunable terahertz two dimensional plasmonic interferometer with an integrated detection element that down converts the terahertz fields to a DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field functioning as the local oscillator. Plasmonic interferometers with two independently tuned paths are studied. These devices demonstrate a means for developing a spectrometer-on-a-chip where the tuning of electrical length plays a role analogous to that of physical path length in macroscopic spectroscopic tools such as Fourier transform interferometers.