  For unimodular gravity, we work out, by using dimensional regularization, the
complete one-loop correction to the graviton propagator in any space-time
dimension. The computation is carried out within the framework where unimodular
gravity has Weyl invariance in addition to the transverse diffeomorphism gauge
symmetry. Thus, no Lagrange multiplier is introduced to enforce the
unimodularity condition. The quantization of the theory is carried out by using
the BRST framework and there considering a large continuous family of
gauge-fixing terms. The BRST formalism is developed in such a way that the set
of ghost, {anti-ghost} and auxiliary fields and their BRST changes do not
depend on the space-time dimension, as befits dimensional regularization. As an
application of our general result, and at D=4, we obtain the renormalized
one-loop graviton propagator in the dimensional regularization minimal
{subtraction} scheme. We do so by considering two simplifying gauge-fixing
choices.
