The first X-ray pulsar, Cen X-3, was discovered 50 yr ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in the presence of the strong magnetic field. Here we present results of the observations of Cen X-3 performed with the Imaging X-ray Polarimetry Explorer. The source exhibited significant flux variability and was observed in two states different by a factor of ∼20 in flux. In the low-luminosity state, no significant polarization was found in either pulse phase-averaged (with a 3σ upper limit of 12%) or phase-resolved (the 3σ upper limits are 20%–30%) data. In the bright state, the polarization degree of 5.8% ± 0.3% and polarization angle of 49.°6 ± 1.°5 with a significance of about 20σ were measured from the spectropolarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anticorrelation between the flux and the polarization degree, as well as strong variations of the polarization angle. The fit with the rotating vector model indicates a position angle of the pulsar spin axis of about 49° and a magnetic obliquity of 17°. The detected relatively low polarization can be explained if the upper layers of the neutron star surface are overheated by the accreted matter and the conversion of the polarization modes occurs within the transition region between the upper hot layer and a cooler underlying atmosphere. A fraction of polarization signal can also be produced by reflection of radiation from the neutron star surface and the accretion curtain.