  Displacement fields are one of the main tuning knobs employed to engineer
flat electronic band dispersions in twisted van der Waals multilayers. Here, we
show that electric fields can also be used to tune the phonon dispersion of
moir\'e superlattices formed by non-centrosymmetric materials, focusing on
twisted transition metal dichalcogenide homobilayers. This effect arises from
the intertwining between the local stacking configuration and the formation of
polar domains within the moir\'e supercell. For small twist angles, increasing
the electric field leads to a universal moir\'e phonon spectrum characterized
by a substantially softened longitudinal acoustic phason mode and a flat
optical phonon mode, both of which cause a significant enhancement in the
vibrational density of states. The phasons also acquire a prominent chiral
character, displaying a nonzero angular momentum spread across the Brillouin
zone. We discuss how the tunability of the moir\'e phonon spectra may affect
electronic properties, focusing on the recently discovered phenomenon of van
der Waals ferroelectricity.
