  We study the effect of random on-site energies on the critical temperature of
a non-interacting Bose gas on a lattice. In our derivation the on-site energies
are distributed according a Gaussian probability distribution function having
vanishing average and variance $v_o^2$. By using the replicated action obtained
by averaging on the disorder, we perform a perturbative expansion for the Green
functions of the disordered system. We evaluate the shift of the chemical
potential induced by the disorder and we compute, for $v_o^2 << 1$, the
critical temperature for condensation. We find that, for large filling,
disorder slightly enhances the critical temperature for condensation.
