We have used the Very Large Array, linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 46 radio stars in the International Celestial Reference Frame (ICRF). Positions were obtained in the ICRF directly through phase referencing of the stars to nearby ICRF quasars whose positions are accurate at the 0.25 mas level. Radio star positions are estimated to be accurate at the 10 mas level, with position errors approaching a few milliarcseconds for some of the stars observed. Our measured positions were combined with previous measurements taken from as early as 1978 to obtain proper-motion estimates for all 46 stars with average uncertainties of ≈1.7 mas yr-1. We compared our radio star positions and proper motions with the Hipparcos Catalogue data and found consistency in the reference frames produced by each data set on the 1 σ level, with errors of ~2.7 mas per axis for the reference frame orientation angles at our mean epoch of 2003.78. No significant spin is found between our radio data frame and the Hipparcos Celestial Reference Frame, with the largest rotation rates of +0.55 and -0.41 mas yr-1 around the x- and z-axes, respectively, with 1 σ errors of 0.36 mas yr-1. Thus, our results are consistent with a nonrotating Hipparcos frame with respect to the ICRF.