The aim of this article is to investigate the performance of near-field integrated sensing and communication (ISAC) systems using rotatable movable antennas (RMAs). In the proposed RMA-enabled system, the positions and rotations of antennas at the base station (BS) are dynamically adjusted to enhance both communication and sensing capabilities. Two designs are explored: i) a sensing-centric design that minimizes the Cram$\text{é}$r-Rao bound (CRB) with signal-to-interference-plus-noise ratio (SINR) constraints, and ii) a communication-centric design that maximizes the sum-rate with a CRB constraint. To solve the formulated optimization problems, two alternating optimization (AO)-based algorithms are proposed capitalizing on the semidefinite relaxation (SDR) method and the particle swarm optimization (PSO) method. Numerical results demonstrate that: i) the proposed RMA-enabled system outperforms the conventional fixed-position antenna and non-rotatable movable antenna systems in both sensing-centric and communication-centric designs and RMAs' rotations show a higher performance gain in communication-centric design; ii) the proposed optimization methods achieve the Pareto boundary in both sensing-centric and communication-centric designs.