We present the study of the dynamical status of the galaxy cluster CL1821+643, a rare and intriguing cool-core cluster hosting a giant radio halo. We base our analysis on new spectroscopic data for 129 galaxies acquired at the Italian Telescopio Nazionale Galileo. We also use spectroscopic data available from the literature and photometric data from the Sloan Digital Sky Survey. We select 120 cluster member galaxies and compute the cluster redshift ˜ 0.296 and the global line-of-sight velocity dispersion σV ˜ 1100 km s-1. The results of our analysis are consistent with CL1821+643 being a massive (M > 1015 M⊙) dynamically relaxed cluster dominated by a big and luminous elliptical at the centre of the cluster potential well. None of the tests employed to study the cluster galaxies kinematics in the 1D (velocity information), 2D (spatial information), and 3D (combined velocity and spatial information) domains is able to detect significant substructures. While this picture is in agreement with previous results based on X-ray data and on the existence of the central cool core, we do not find any evidence of a merging process responsible for the radio halo discovered in this cluster. Thus, this radio halo remains an open problem that raises doubts about our understanding of diffuse radio sources in clusters.