  We consider a three-dimensional rotating Ho\v{r}ava AdS black hole, that
corresponds to a Lorentz-violating version of the BTZ black hole and we analyze
the effect of the breaking of Lorentz invariance on the possibility that the
black hole can acts as a particle accelerator by analyzing the energy in the
center of mass (CM) frame of two colliding particles in the vicinity of its
horizons. We find that the critical angular momentum of particles increases
when the Ho\v{r}ava parameter $\xi$ increases and when the aether parameter $b$
increases. Also, the particles can collide on the inner horizon with
arbitrarily high CM energy if one of the particles has a critical angular
momentum being possible the BSW process, for the non-extremal rotating
Ho\v{r}ava AdS black hole. Mainly, while that for the extremal BTZ black hole
the particles with critical angular momentum only can exist on the degenerate
horizon, for the Lorentz-violating version of the BTZ black hole the particle
with critical angular momentum can exist in a region from the degenerate
horizon.
