  We study the collision property of spinning particles near a
Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. Our results show that although
the center-of-mass energy of two ingoing particles diverges if one of the
particles possesses a critical angular momentum, however, particle with
critical angular momentum can not exist outside of the horizon due to the
violation of timelike constraint. Further detailed investigation indicates that
only the particle with a subcritical angular momentum is allowed to exist near
an extremal rotating BTZ black hole and the corresponding collision
center-of-mass energy can be arbitrarily large in a critical angular momentum
limit.
