  We show that Weyl semimetals exhibit a mixed axial-torsional anomaly in the
presence of axial torsion, a concept exclusive of these materials with no known
natural fundamental interpretation in terms of the geometry of spacetime. This
anomaly implies a nonconservation of the axial current---the difference in
current of left- and right-handed chiral fermions---when the torsion of the
spacetime in which the Weyl fermions move couples with opposite sign to
different chiralities. The anomaly is activated by driving transverse sound
waves through a Weyl semimetal with a spatially varying tilted dispersion,
which can be engineered by applying strain. This leads to sizable alternating
current in presence of a magnetic field that provides a clear-cut experimental
signature of our predictions.
