The dissipation of turbulent gas motions is one of the likely mechanisms that has been proposed to heat the intracluster medium (ICM) in the cores of clusters and groups of galaxies. We consider the impact of gas motions on the width of the most prominent X-ray emission lines. For heavy elements (like iron) the expected linewidth is much larger than the width due to pure thermal broadening and the contribution due to turbulent gas motions should be easily detected with the new generation of X-ray micro-calorimeters, such as the Spektr-RG calorimeter (SXC). For instance in the Perseus cluster the turbulent velocity required to balance radiative cooling (as derived by Rebusco et al. 2006), would imply a width of the 6.7 keV Fe line of 10-20 eV, while the pure thermal broadening is ~4 eV. The radial dependence of the linewidth is sensitive to i) the radial dependence of the velocity amplitude and ii) the "directionality" of the stochastic motions (e.g. isotropic turbulence or predominantly radial gas motions). If the width of several lines, characteristic for different gas temperatures, can be measured, then it should be possible to probe both the "directionality" and the amplitude of the gas motions. Moreover a measurement of the width would put a lower limit on the amount of the kinetic energy available for dissipation, giving a constraint on the ICM models.