We use near-infrared dynamic multiple scattering of light [diffusing-wave spectroscopy (DWS)] to detect the activation of the somato-motor cortex in 11 right-handed volunteers performing a finger opposition task separately with their right and left hands. Temporal autocorrelation functions of the scattered light field are measured during periods of motor task alternating with resting baseline periods. From an analysis of the experimental data with an analytical theory for from a three-layer geometry with optical and dynamical heterogeneity representing scalp, skull, and cortex, we obtain quantitative estimates of the diffusion coefficient in cortical regions. Consistent with earlier results, the measured cortical diffusion coefficient is found to be increased during the motor task, with a strong contralateral and a weaker ipsilateral increase consistent with the known brain hemispheric asymmetry for right-handed subjects. Our results support the interpretation of the increase of the cortical diffusion coefficient during finger opposition being due to the functional increase in cortical blood flow rate related to vasodilation.