  Gravitational radiation-reaction phenomena occurring in the dynamics of
inspiralling compact binary systems are investigated at the first
post-Newtonian order beyond the quadrupole approximation in the context of
Einstein-Cartan theory, where quantum spin effects are modeled via the
Weyssenhoff fluid. We exploit balance equations for the energy and angular
momentum to determine the binary orbital decay until the two bodies collide.
Our framework deals with both quasi-elliptic and quasi-circular trajectories,
which are then smoothly connected. Key observables like the laws of variation
of the orbital phase and frequency characterizing the quasi-circular motion are
derived analytically. We conclude our analysis with an estimation of the spin
contributions at the merger, which are examined both in the time domain and the
Fourier frequency space through the stationary wave approximation.
