  We propose that resonant inelastic X-ray scattering (RIXS) is an effective
probe of the fractionalized excitations in three-dimensional (3D) Kitaev spin
liquids. While the non-spin-conserving RIXS responses are dominated by the
gauge-flux excitations and reproduce the inelastic-neutron-scattering response,
the spin-conserving (SC) RIXS response picks up the Majorana-fermion
excitations and detects whether they are gapless at Weyl points, nodal lines,
or Fermi surfaces. As a signature of symmetry fractionalization, the SC RIXS
response is suppressed around the $\Gamma$ point. On a technical level, we
calculate the exact SC RIXS responses of the Kitaev models on the
hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices,
arguing that our main results also apply to generic 3D Kitaev spin liquids
beyond these exactly solvable models.
