  In this paper we investigate the gravitational-wave generation problem at the
first post-Newtonian order in the context of Einstein-Cartan theory by
exploiting the Blanchet-Damour formalism. The quantum intrinsic spin carried by
slowly moving, weakly stressed, weakly self-gravitating sources is described
geometrically by means of the torsion tensor. We obtain the expression of the
source multipole moments with the required accuracy. The analysis of the
physical meaning of the lowest-order non-radiative moments and of the
asymptotic gravitational waveform is also performed. Eventually, we draw our
conclusions and estimate the order of magnitude of the spin contributions in
the gravitational-wave signal.
