We determine rotation periods of a sample of 48 late F-type to mid-M dwarf stars using time series high-resolution spectroscopy of the Ca II H&K and H α chromospheric activity indicators. We find good agreement between the rotation periods obtained from each of these two indicators. An empirical relationship between the level of chromospheric emission measured by log _{10}(R^' }_HK) and the spectroscopic rotation periods is reported. This relation is largely independent of the spectral type and the metallicity of the stars and can be used to make a reliable prediction of rotation periods for late K to mid-M dwarfs with low levels of activity. For some stars in the sample, the measured spectroscopic rotation periods coincide, or are very close, to the orbital periods of postulated planets. In such cases, further studies are needed to clarify whether the associated periodic radial velocity signals reveal the existence of planets or are due to magnetic activity.