We present a set-up for proton computed tomography (pCT), composed of a microstrip silicon tracker and a YAG:Ce calorimeter, able to directly measure the relative stopping power (RSP) maps to be used in hadron therapy. The system, tested with an electron density phantom at the Trento proton Therapy Center, is able to correlate measured and expected RSP with discrepancies of the order of 1% or less. Furthermore, pCT tomographies of an anthropomorphous head phantom taken with our device, when compared with x-ray CT images of the same object, evidence a significant reduction of artifacts induced by titanium spinal bone prosthesis and tungsten dental filling.