  Calibrating the strength of the light-matter interaction is an important
experimental task in quantum information and quantum state engineering
protocols. The strength of the off-resonant light-matter interaction in
multi-atom spin oscillators can be characterized by the coupling rate
$\Gamma_\text{S}$. Here we utilize the Coherently Induced Faraday Rotation
(CIFAR) signal for determining the coupling rate. The method is suited for both
continuous and pulsed readout of the spin oscillator, relying only on applying
a known polarization modulation to the probe laser beam and detecting a known
optical polarization component. Importantly, the method does not require
changes to the optical and magnetic fields performing the state preparation and
probing. The CIFAR signal is also independent of the probe beam photo-detection
quantum efficiency, and allows direct extraction of other parameters of the
interaction, such as the tensor coupling $\zeta_\text{S}$, and the damping rate
$\gamma_\text{S}$. We verify this method in the continuous wave regime, probing
a strongly coupled spin oscillator prepared in a warm cesium atomic vapour.
