The barbs or legs of some prominences show an apparent motion of rotation, which are often termed solar tornadoes. It is under debate whether the apparent motion is a real rotating motion, or caused by oscillations or counter-streaming flows. We present analysis results from spectroscopic observations of two tornadoes by the Interface Region Imaging Spectrograph. Each tornado was observed for more than 2.5 hr. Doppler velocities are derived through a single Gaussian fit to the Mg II k 2796 angstrom and Si IV 1393 angstrom. line profiles. We find coherent and stable redshifts and blueshifts adjacent to each other across the tornado axes, which appears to favor the interpretation of these tornadoes as rotating cool plasmas with temperatures of 10(4) K-10(5) K. This interpretation is further supported by simultaneous observations of the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, which reveal periodic motions of dark structures in the tornadoes. Our results demonstrate that spectroscopic observations can provide key information to disentangle different physical processes in solar prominences.