We present the first non-resonant and non-enhanced Raman correlation spectroscopy experiments. They are conducted on a confocal microscope combined with a Raman spectrometer. The thermal fluctuations of the Raman intensities scattered by dispersions of polystyrene particles of sub-micrometric diameters are measured and analysed by deriving the autocorrelation functions (ACFs) of the intensities. We show that for particles of diameter down to 200 nm, RCS measurements are successfully obtained in spite of the absence of any source of amplification of the Raman signal. For particles of diameter ranging from 200 to 750 nm, the ACFs present a time-decay behaviour in accordance with the model of free Brownian particles. For particles of 1000 nm in diameter, the AFCs present a different behaviour with a much smaller characteristic time. This results from the dynamics of a single-Brownian particle trapped in the confocal volume by the optical forces of the focus spot.