Attempts carried out in the past to detect linear or circular polarization of the Cosmic Microwave Background (CMB) radiation have produced only upper limits to the degree of polarization. These limits are at least two orders of magnitude above the expected value of few times 10 -6 or less, as suggested by models combined with the measured values of the CMB anisotropy. Because detection of polarization of the Cosmic Microwave Background will improve our knowledge of the phenomena which accompanied the evolution of the Universe, we built a polarimeter whose sensitivity, 2.1 t(S) mK, is sufficient to detect linear or circular polarization at level of few μK. Details of the system are presented. A testing campaign carried out with a partial prototype of our polarimeter, in a noisy environment, gave an upper limit to the degree of linear polarization of the CMB on angular scales of 14° of ∼8 · 10 -5, comparable to the limits at similar angular scales so far published.