It is shown that the recently detected acceleration of the universe can be understood by considering a modification of the teleparallel equivalent of General Relativity (TEGR), with no need of dark energy. The solution also exhibits phases dominated by matter and radiation as expected in the standard cosmological evolution. We perform a joint analysis with measurements of the most recent type Ia supernovae (SNe Ia), Baryon Acoustic Oscillation (BAO) peak and estimates of the CMB shift parameter data to constraint the only new parameter this theory has.