  We report non-invasive detection of spin coherence in a collection of
Raman-driven cold atoms using dispersive Faraday rotation fluctuation
measurements, which opens up new possibilities of probing spin correlations in
quantum gases and other similar systems. We demonstrate five orders of
magnitude enhancement of the measured signal strength than the traditional spin
noise spectroscopy with thermal atoms in equilibrium. Our observations are in
good agreement with the comprehensive theoretical modeling of the driven atoms
at various temperatures. The extracted spin relaxation rate of cold rubidium
atoms with atom number density $\sim$10$^9/$cm$^3$ is of the order of
2$\pi\times$0.5 kHz at 150 $\mu$K, two orders of magnitude less than $\sim$
2$\pi\times$50 kHz of a thermal atomic vapor with atom number density
$\sim$10$^{12}/$cm$^3$ at 373 K.
