A concept for high precision astrometry with a conventional wide field telescope is presented, enabling a space telescope to perform simultaneously coronagraphic imaging of exoplanets, astrometric measurement of their orbits and masses, and deep wide field imaging for a wide range of astrophysical investigations. Our concept uses a diffractive telescope pupil (primary mirror), obtained by placing a regular grid of small sub millimeter spots on the primary mirror coating. When the telescope is pointed at a bright star, the wide field image contains both a large number of background stars used for astrometric referencing, and faint diffraction spikes created by the grid of dots on the primary mirror. The diffraction spikes encode instrumental astrometric distortions due to optics or the detector, allowing precise measurement of the central star against a large number of faint background stars. With up to a few percent of the primary mirror area covered by the dots, the fraction of the central starlight located in the diffraction spikes is kept sufficiently small to allow full sensitivity deep imaging over the telescope's field of view. Since the dots are regularly spaced, they do not diffract light at small angular separations, and therefore allow full coronagraphic imaging capability. We show that combining simultaneous astrometric and coronagraphic measurements allows improved detection and characterization of exoplanets by constraining the planet(s) characteristics with both measurements. Our preliminary astrometric accuracy error budget shows that sub-micro arcsecond astrometry can be achieved with a 1.4 m diameter telescope, and that astrometric accuracy improves rapidly with telescope diameter.