A Friedmann like cosmological model in Einstein–Cartan framework is studied when the torsion function is assumed to be proportional to a single phi (t) function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with phi (t)=- alpha H(t) big ({rho _{m}(t)}/{rho _{0c}}big )^n is totally compatible with recent cosmological data, where alpha and n are free parameters to be constrained from observations, rho _m is the matter energy density and rho _{0c} the critical density. The recent accelerated phase of expansion of the universe is correctly reproduced by the contribution coming from torsion function, with a deceleration parameter indicating a transition redshift of about 0.65.