  We perform a Monte Carlo Renormalization Group analysis of the critical
behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with
Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to
the calculation of the critical temperature $T_c$ and the magnetic
eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections
hinder the calculation of the temperature eigen-exponent $y_t$. At last, the
results are shown to be consistent with a finite size scaling analysis.
