A core challenge in physical-layer security is the difficulty of obtaining the channel state information (CSI) of potential eavesdroppers. The inherent sensing functionality of integrated sensing and communication (ISAC) systems offers a promising solution by enabling the estimation of key parameters, such as the eavesdropper's angles of departure (AoDs). Capitalizing on this capability, we propose a sensing-assisted secure communication scheme for a movable antenna (MA)-aided ISAC system. The scheme comprises two stages: eavesdropper AoD sensing and secure communication. In the first stage, the base station (BS) optimizes the positions of its transmit and receive MAs to enhance sensing accuracy. We derive the closed-form Cramer-Rao bound (CRB) for the estimated AoDs to fundamentally characterize how MA positions influence the estimation uncertainty. In the second stage, the BS ensures secure communication by designing a robust beamforming vector that accounts for the AoD uncertainty region and by further optimizing the transmit MAs' positions to maximize the secrecy rate. To manage the end-to-end design, we formulate a joint optimization problem. This intractable non-convex problem is decomposed into two subproblems. For the first subproblem, we develop an alternating optimization (AO) algorithm to solve the CRB minimization problem. For the second subproblem, we solve the worst-case secrecy rate maximization problem using a method based on backward induction, convex hull construction, and AO. Finally, simulation results are provided to demonstrate the significant advantages of the proposed scheme compared to various benchmarks.