  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 $0.65$.
