This paper investigates the effects of gravitational radiation-reaction forces on the dynamics of inspiraling compact binary systems at the first post-Newtonian (1PN) order in Einstein-Cartan (EC) theory. The authors use the Weyssenhoff fluid to model quantum spin effects and employ balance equations for energy and angular momentum to determine the orbital decay until the binary collides. The study covers both quasi-elliptic and quasi-circular trajectories, which are smoothly connected. Key observables, such as the laws of variation of the orbital phase and frequency, are derived analytically. The analysis also estimates the spin contributions at the merger, examining them in both the time domain and the Fourier frequency space through the stationary wave approximation. The results provide insights into the behavior of compact binary systems influenced by back-reaction forces and highlight the differences between EC theory and General Relativity (GR) in the context of gravitational wave astronomy.This paper investigates the effects of gravitational radiation-reaction forces on the dynamics of inspiraling compact binary systems at the first post-Newtonian (1PN) order in Einstein-Cartan (EC) theory. The authors use the Weyssenhoff fluid to model quantum spin effects and employ balance equations for energy and angular momentum to determine the orbital decay until the binary collides. The study covers both quasi-elliptic and quasi-circular trajectories, which are smoothly connected. Key observables, such as the laws of variation of the orbital phase and frequency, are derived analytically. The analysis also estimates the spin contributions at the merger, examining them in both the time domain and the Fourier frequency space through the stationary wave approximation. The results provide insights into the behavior of compact binary systems influenced by back-reaction forces and highlight the differences between EC theory and General Relativity (GR) in the context of gravitational wave astronomy.