Context. CMB experiments aiming at a precise measurement of the CMB polarization, such as the Planck satellite, need a strong polarized absolute calibrator on the sky to accurately set the detectors polarization angle and the cross-polarization leakage. As the most intense polarized source in the microwave sky at angular scales of few arcminutes, the Crab nebula will be used for this purpose. Aims. Our goal was to measure the Crab nebula polarization characteristics at 90 GHz with unprecedented precision. Methods. The observations were carried out with the IRAM 30 m telescope employing the correlation polarimeter XPOL and using two orthogonally polarized receivers. Results. We processed the Stokes I, Q, and U maps from our observations in order to compute the polarization angle and linear polarization fraction. The first is almost constant in the region of maximum emission in polarization with a mean value of αSky = 152.1±0.3° in equatorial coordinates, and the second is found to reach a maximum of Π = 30% for the most polarized pixels. We find that a CMB experiment having a 5 arcmin circular beam will see a mean polarization angle of αSky = 149.9±0.2° and a mean polarization fraction of Π = 8.8±0.2%.