  Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes
in semiconductor nanowires proximity coupled to a superconductor. We track the
evolution of the induced superconducting gap in InSb nanowires coupled to a
NbTiN superconductor in a large range of magnetic field strengths and
orientations. Based on realistic simulations of our devices, we reveal SOI with
a strength of 0.15-0.35 eV$\require{mediawiki-texvc}\AA$. Our approach
identifies the direction of the spin-orbit field, which is strongly affected by
the superconductor geometry and electrostatic gates.
