  We show that a Weyl superconductor can absorb light via a novel
surface-to-bulk mechanism, which we dub the topological anomalous skin effect.
This occurs even in the absence of disorder for a single-band superconductor,
and is facilitated by the topological splitting of the Hilbert space into bulk
and chiral surface Majorana states. In the clean limit, the effect manifests as
a characteristic absorption peak due to surface-bulk transitions. We also
consider the effects of bulk disorder, using the Keldysh response theory. For
weak disorder, the bulk response is reminiscent of the Mattis-Bardeen result
for $s$-wave superconductors, with strongly suppressed spectral weight below
twice the pairing energy, despite the presence of gapless Weyl points. For
stronger disorder, the bulk response becomes more Drude-like and the $p$-wave
features disappear. We show that the surface-bulk signal survives when combined
with the bulk in the presence of weak disorder. The topological anomalous skin
effect can therefore serve as a fingerprint for Weyl superconductivity. We also
compute the Meissner response in the slab geometry, incorporating the effect of
the surface states.
