We derive the astrometric orbit of the photo- center of the close pair α UMi AP (= α UMi Aa) of the Polaris multiple stellar system. The orbit is based on the spectroscopic orbit of the Cepheid α UMi A (orbital period of AP: 29.59 years), and on the difference ∆μ between the quasi-instantaneously measured HIPPARCOS proper motion of Polaris and the long-term-averaged proper motion given by the FK5. There remains an ambiguity in the inclination i of the orbit, since ∆μ cannot distinguish between a prograde orbit (i = 50 .̂1) and a retrograde one (i = 130 .̂2). Available photographic observations of Polaris favour strongly the retrograde orbit. For the semi-major axis of the photo-center of AP we find about 29 milliarcsec (mas). For the component P, we estimate a mass of 1.5 M☉ and a magnitude difference with respect to the Cepheid of 6.5 mag. The present separation between A and P should be about 160 mas. We obtain the proper motion of the center-of-mass of α UMi AP with a mean error of about 0.45 mas/year. Using the derived astrometric orbit, we find the position of the center-of-mass at the epoch 1991.31 with an accuracy of about 3.0 mas. Our ephemerides for the orbital correction, required for going from the position of the center-of-mass to the instantaneous position of the photo-center of AP at an arbitrary epoch, have a typical uncertainty of 5 mas. For epochs which differ from the HIPPARCOS epoch by more than a few years, a prediction for the actual position of Polaris based on our results should be significantly more accurate than using the HIPPARCOS data in a linear prediction, since the HIPPARCOS proper motion contains the instantaneous orbital motion of about 4.9 mas/year = 3.1 km/s. Finally we derive the galactic space motion of Polaris.