  We present a Monte Carlo collisional scheme that models single Compton
scattering between leptons and photons in particle-in-cell codes. The numerical
implementation of Compton scattering can deal with macro-particles of different
weights and conserves momentum and energy in each collision. Our scheme is
validated through two benchmarks for which exact analytical solutions exist:
the inverse Compton spectra produced by an electron scattering with an
isotropic photon gas and the photon-electron gas equilibrium described by the
Kompaneets equation. It opens new opportunities for numerical investigation of
plasma phenomena where a significant population of high energy photons is
present in the system.
