With a neutron spin-echo reflectometer (OffSpec at ISIS, UK) it is possible to measure the gravitation-induced quantum phase difference between the two spin states of the neutron wave function in a magnetic field. In the small-angle approximation, this phase depends linearly on the inclination angle of the neutron beam with respect to the horizontal. This also holds for the Bonse-Hart interferometer used in the Colella-Overhauser-Werner experiments and should be taken into account. Neglecting this term could yield deviations up to 1% per degree inclination angle. The gravitation-induced quantum phase as measured with OffSpec with an accuracy of 0.1% agrees with the theoretically expected results.