Integrated sensing and communication (ISAC) has recently emerged as a viable technique for establishing sensing and communication using the same resources. Nonetheless, the operation of ISAC networks is often challenged by the absence of a direct link between the sensing node and the targets, and by the risk of disclosing confidential data to malicious targets when using the same signal for both tasks. In this paper, a robust reconfigurable intelligent surface (RIS)-aided scheme for securing a full-duplex (FD) ISAC network is proposed. The considered network consists of uplink and downlink users served in FD through a multi-antenna dual-functional radar communication base station (BS), which employs co-located multi-antenna communication-radar arrays to detect multiple malicious targets while preserving communication secrecy in their presence. Additionally, the BS utilizes an optimized artificial noise (AN) that serves to disrupt the malicious targets' reception and increase the sensing power. By optimally designing the RIS phase shifts, transmit beamforming, AN covariance, and uplink users' transmit power and combining vectors using an alternating optimization-based algorithm, the network's sensing performance is maximized under secrecy and total power constraints. Numerical results present the proposed scheme's efficacy, particularly when a direct link between the BS and the various nodes/targets is absent.