The study of measurable effects in non-inertial reference frames in quantum physics has been paid a great deal of attention to in recent decades, since one must inevitably deal with the effects of gravity and rotation in microscopic dimensions for a better understanding of nature. In this field neutron physics has played a prominent role in the past, as the COW (Colella - Overhauser - Werner) - experiment and the measurement of the Sagnac effect have impressively demonstrated. In 1988, Mashhoon [Phys. Rev. Lett. 61, 2639 (1988)] predicted a new relativistic quantum mechanical effect, i.e. a coupling of spin with the angular velocity of a rotating reference system. Following the prediction, the spin-rotation interaction has been successfully derived from the Dirac theory, a concrete measurement however is still missing. The first proposal in this regard included a measurement via neutron-interferometry. In this thesis an experimental study of spin-rotation coupling is described. The original idea of the experiment by Mashhoon has been adapted to a set-up using a neutron polarimeter. This measurement method has advantages over neutron-interferometry, in particular because of higher insensitivity to ambient disturbances. Experimental parameters, such as dimensions of various coils for spin-manipulation, were determined and a set-up was constructed. In the first measurement, problems with stray fields were encountered. In order to avoid them, two DC-coils were added to the original polarimeter arrangement. The final results show that a phase shift due to an interaction of angular velocity of a rotating magnetic field and spin could be measured successfully and agree well with theoretical predictions.