Pinching-antenna systems (PASs) have recently emerged as a flexible, cost-effective route to large-scale antenna deployments envisioned for integrated sensing and communications (ISAC). This paper establishes the fundamental sensing limits of a bistatic PAS link by deriving closed-form Cramér-Rao lower bounds for the joint estimation of range and direction when a target is illuminated by pinching antennas placed along a dielectric waveguide and observed by a uniform linear array receiver. By rigorously preserving the amplitude and phase variations of each pinching antenna, as well as exploiting their non-uniform deployment, we gain valuable insights into the performance gain of PASs over conventional antenna arrays. Numerical results validate that the PAS-based ISAC can achieve centimeter-level ranging and sub-degree angular resolution with significantly fewer hardware resources than conventional uniform linear arrays. The derived bounds provide practical design guidelines for next-generation PAS-enabled ISAC systems.