A Coulomb polarimeter primarily to determine the nuclear polarization of a polarized 23Na beam is described. Coulomb excitation of 23Na to its first excited state is used. The excited projectiles are identified by coincidences between inelastically scattered particles and deexcitation γ-rays. First results obtained with the polarimeter are in agreement with former experiments for the second rank tensor polarization of such a beam. The first rank tensor polarization of a polarized 23Na beam could be measured as well.