  Electrons commonly couple through Fr\"ohlich interactions with longitudinal
optical phonons to form polarons. However, trions possess a finite angular
momentum and should therefore couple instead to rotational optical phonons.
This creates a polaronic trion whose binding energy is determined by the
crystallographic orientation of the lattice. Here, we demonstrate theoretically
within the Fr\"ohlich approach and experimentally by photoluminescence emission
that the bare trion binding energy (20 meV) is significantly enhanced by the
phonons at the interface between the two-dimensional semiconductor MoS$_2$ and
the bulk transition metal oxide SrTiO$_3$. The low-temperature {binding energy}
changes from 60 meV in [001]-oriented substrates to 90 meV for [111]
orientation, as a result of the counter-intuitive interplay between the
rotational axis of the MoS$_2$ trion and that of the SrTiO$_3$ phonon mode.
