In the paper, it has been proposed a calculation algorithm that allows obtaining the value of the Sivers asymmetry in semi-inclusive deep inelastic scattering of charged leptons on a transversely polarized proton using the event generator PYTHIA8 and the StringSpinner plug-in. The calculation was performed in the kinematics of the COMPASS experiment: a muon with an energy of 160 GeV scatters on a stationary proton target. The proposed algorithm was shown to make it possible to estimate high accurately the Sivers asymmetry of the final hadron.