  The teleparallel $T_{4}$ version of Riemannian geometry of acoustic spacetime
in rotating $2-D$ Bose-Einstein condensates (BEC) is investigated. An
experiment is proposed on the basis of phonon ray trajectory around a vortex.
The deviation geodesic equation may be expressed in terms of Cartan acoustic
torsion. The Riemann curvature is computed in terms of rotation of the fluid.
The geodesic deviation equation shows that the acoustic torsion acts locally as
a diverging lens and the stream lines on opposite sides of the BEC vortex flow
apart from each other. We also show that the Magnus field is cancelled when the
acoustic torsion coincides with the rotation of the condensate. This effect is
equivalent to the Meissner effect in superconductors. It is interesting to note
how the teleparallel acoustic spacetime constrains the physical parameters in
the BEC. Here we use the term acoustic torsion since in teleparallelism it is
derived from the acoustic metric.
