Time-reversal techniques have been demonstrated to be able to reverse the incoherence that usually characterizes the field distribution within reverberation chambers. Its ability of generating coherent pulsed fields has previously been applied to communications as well as the generation of controlled wavefronts for immunity testing. Nevertheless, the issue of polarization has not yet received due attention. We prove in this paper that time-reversal techniques, when applied to reverberating media, also allow controlling the polarization of the focused pulsed fields. This result, although apparently paradoxical, relies on the very incoherence properties of reverberation chambers. Remarkably, this allows to generate fields with any polarization by using one single static excitation antenna, enabling a changing polarization just by modifying the signal driving it. A theoretical model is proposed for proving this feature, together with experimental results validating it. Cross-polarization rejections much higher than 20 dB are observed, making the quality of the generated pulses comparable to those obtained in anechoic chambers. Interestingly, the cross-polarization rejection is not expected to depend on that of the transmission antenna as measured in a freespace environment, but just on the properties of reverberation chambers and the frequency bandwidth of the pulse.