  We analytically study the quasinormal modes of a scalar perturbation around a
rotating BTZ-like black hole in the Einstein-bumblebee gravity. We observe that
the Lorentz symmetry breaking parameter imprints only in the imaginary parts of
the quasinormal frequencies for the right-moving and left-moving modes. The
perturbational field decays more rapidly for the negative Lorentz symmetry
breaking parameter, but more slowly for the positive one. The forms of the real
parts are the same as those in the usual BTZ black holes. Moreover, we also
discuss the $AdS/CFT$ correspondence from the quasinormal modes and find that
the Lorentz symmetry breaking parameter enhances the left and right conformal
weights $h_L$ and $h_R$ of the operators dual to the scalar field in the
boundary. These results could be helpful to understand the $AdS/CFT$
correspondence and the Einstein-bumblebee gravity with the Lorentz symmetry
violation.
