We present interferometric maps of the RW~Aur system obtained with the IRAM Plateau de Bure Interferometer in CO(2-1), CO(1-0), and nearby continuum. The sub-arcsecond angular resolution (0.89'' x 0.58'') and high-sensitivity reached at 1.3mm enable us to resolve three molecular structures: (1) an optically thick disk around RWAur A in rotation about the optical jet axis, (2) a disturbed asymmetric peak around RWAur B, (3) a 600 AU-long ``arm'' of material trailing from the RWAur A disk. Comparison with Keplerian models indicate that the RWAur A disk is the smallest detected so far around a T Tauri star (radius 40-57 AU) and that the CO emitting layer at the outer edge is warmer than the dust (T ~ 60-100 K) and relatively thick (Nwarm ~ 0.1-10 x 1e22 cm-2). The morphology and kinematics of the detected features strongly suggest that we are witnessing tidal stripping of the primary disk by the recent fly-by of RWAur B. We speculate that tidal dissipation might explain the warmer gas temperatures in the RWAur A disk compared with typical T Tauri stars, and perhaps play a role in its elevated accretion rate. We also find that the rotation sense of the RWAur A disk is opposite to transverse velocity shifts in the optical jet reported by Woitas et al. (2005). We argue that these transverse shifts are likely to represent only upper limits to the true jet rotation speed. The limits remain consistent with current models of MHD launching from the disk.