A twistor model is proposed for the free relativistic anyon. The Hamil
tonian reduction of this model by the action of the spin generator lea
ds to the minimal covariant model; whereas that by the action of spin
and mass generators leads to the anyon model with free phase space whi
ch is a cotangent bundle of the Lobachevsky plane with twisted symplec
tic structure. Quantum mechanics of that model is described by irreduc
ible representations of the (2+1)-dimensional Poincare group.