In this paper, we investigate an active-RIS (ARIS)-aided integrated sensing and communication (ISAC) system with Rydberg Atomic REceiver (RARE). Leveraging the magnitude-only and real-domain observation structure of RARE, we first derive a unified ISAC model, along with a closed-form Cramer-Rao bound (CRB) for direction-of-arrival (DoA) estimation. Based on this formulation, we propose a joint design of the {base station (BS)} beamforming and ARIS reflection coefficients to minimize the CRB under RARE-specific signal-to-interference-noise-ratio (SINR) and ARIS power constraints. To tackle the resulting highly non-convex problem, we develop an alternating optimization (AO) framework that combines semidefinite relaxation (SDR) for beamforming and a majorization-minimization (MM)-based approach for ARIS design. Numerical results demonstrate that the proposed RARE-aware framework significantly outperforms conventional RF-based designs and achieves performance close to the radar-only benchmark, highlighting the potential of RARE for quantum-enhanced ISAC with ARIS.