We consider a three-dimensional rotating AdS black hole, which is a solution of Hoava gravity in the low-energy limit 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 act 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 Hoava 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, possible for the BSW process. Here it is essential that, while 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 away from the degenerate horizon. It is worth mentioning that the results exposed in this manuscript can be applied for the covariant version of Hoava gravity, where the covariant definition of the center-of-mass energy is well defined.