We present the obliquity of the warm Neptune HD 106315c measured via a series of spectroscopic transit observations. HD 106315c is a 4.4 REarth warm Neptune orbiting a moderately rotating late F star with a period of 21.05 days. HD 106315 also hosts a 2.5 REarth super-Earth on a 9.55 day orbit. Our Doppler tomographic analyses of four transits observed by the Magellan/MIKE, HARPS, and TRES facilities find HD 106315c to be in a low stellar obliquity orbit, consistent with being well aligned with the spin axis of the host star at . We suggest, via dynamical N-body simulations, that the two planets in the system must be coplanar, and thus are both well aligned with the host star. HD 106315 is only the fourth warm Neptune system with obliquities measured. All warm Neptune systems have been found in well aligned geometries, consistent with the interpretation that these systems are formed in situ in the inner protoplanetary disk, and also consistent with the majority of Kepler multi-planet systems that are in low obliquity orbits. With a transit depth of 1.02 mmag, HD 106315c is among the smallest planets to have been detected in transit spectroscopy, and we discuss its detection in the context of TESS and the next generations of spectrographs.