  We calculate perturbatively the effect of a dipolar interaction upon the
Bose-Einstein condensation temperature. This dipolar shift depends on the angle
between the symmetry axes of the trap and the aligned atomic dipole moments,
and is extremal for parallel or orthogonal orientations, respectively. The
difference of both critical temperatures exhibits most clearly the
dipole-dipole interaction and can be enhanced by increasing both the number of
atoms and the anisotropy of the trap. Applying our results to chromium atoms,
which have a large magnetic dipole moment, shows that this dipolar shift of the
critical temperature could be measured in the ongoing Stuttgart experiment.
