  The quark spin effects are introduced for the first time in the string
fragmentation routine of the Pythia 8 Monte Carlo event generator for the
simulation of $e^+e^-$ annihilation to hadrons. To describe the spin effects
the string+${}^3P_0$ model of polarized hadronization with emissions of
pseudoscalar and vector mesons is used. The spin effects are activated in the
generator by extending the StringSpinner package, previously applied to the
simulation of deep inelastic scattering off a polarized nucleon. The generator
is used to carry out simulations of $e^+e^-$ annihilation at the center of mass
energy of $10.6\,\rm{GeV}$. The Collins asymmetry for back-to-back pion pairs
is evaluated and compared to the asymmetry as measured by the BELLE experiment.
A satisfactory agreement is found.
