  We investigate the critical temperature of an interacting Bose gas confined
in a trap described by a generic isotropic power-law potential. We compare the
results with respect to the non-interacting case. In particular, we derive an
analytical formula for the shift of the critical temperature holding to first
order in the scattering length. We show that this shift scales as $N^{n\over
3(n+2)}$, where $N$ is the number of Bosons and $n$ is the exponent of the
power-law potential. Moreover, the sign of the shift critically depends on the
power-law exponent $n$. Finally, we find that the shift of the critical
temperature due to finite-size effects vanishes as $N^{-{2n\over 3(n+2)}}$.
