The planetary ephemeris is an essential tool for interplanetary spacecraft navigation, studies of solar system dynamics (including, for example, barycenter corrections for pulsar timing ephemeredes), the prediction of occultations, and tests of general relativity. We are carrying out a series of astrometric VLBI observations of the Cassini spacecraft currently in orbit around Saturn, using the Very Long Baseline Array (VLBA). These observations provide positions for the center of mass of Saturn in the International Celestial Reference Frame (ICRF) with accuracies ~0.3 milli-arcsecond (1.5 nrad), or about 2 km at the average distance of Saturn. This paper reports results from eight observing epochs between 2006 October and 2009 April. These data are combined with two VLBA observations by other investigators in 2004 and a Cassini-based gravitational deflection measurement by Fomalont et al. in 2009 to constrain a new ephemeris (DE 422). The DE 422 post-fit residuals for Saturn with respect to the VLBA data are generally 0.2 mas, but additional observations are needed to improve the positions of all of our phase reference sources to this level. Over time we expect to be able to improve the accuracy of all three coordinates in the Saturn ephemeris (latitude, longitude, and range) by a factor of at least three. This will represent a significant improvement not just in the Saturn ephemeris but also in the link between the inner and outer solar system ephemeredes and in the link to the inertial ICRF.