We present an optical system which integrates a plasmonic sensing surface and an angular tracking system to enable a compact refractive index measurement. A refractive index change at the surface of the sensing membrane causes a change in the angle at which monochromatic light is transmitted through the membrane. This transmission angle is measured by the angular tracking system. We show good theoretical and experimental agreement of the transmission of the plasmonic sensing surface at different angular illumination of the membranes. Using this compact optical setup the embedded angular tracking system has an accuracy of <10(-4) deg. This corresponds to a sensitivity <10(-5) refractive index units. Finally we demonstrate this measurement technique using different concentrations of saline solution.