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We present a semi-empirical effective Hamiltonian to capture effects of disorder associated with Ba and Sr cations occupying A sites in (Ba_xSr_1-x)TiO₃ on its ferroelectric phase transition. Averaging between the parameters of firstprinciples effective Hamiltonians of end members BaTiO₃ and SrTiO₃, we include a term with an empirical parameter to capture the local polarization and strains arising from the difference between ionic radii of Ba and Sr. Using mixed-space molecular dynamics of the effective Hamiltonian, we determine T-dependent ferroelectric phase transitions in (Ba_xSr_1-x)TiO₃ which are in good agreement with experiment. Our scheme of determination of semi-empirical parameters in effective Hamiltonian should be applicable to other perovskite-type ferroelectric solid solutions.