Integrated satellite-terrestrial edge computing networks have emerged as a promising solution to enhance data processing capabilities and connectivity in remote and underserved areas. However, the physical layer security of computation offloading in such networks is increasingly challenged by potential eavesdroppers. In this paper, we propose an integrated sensing and communication (ISAC) empowered secure computation offloading in integrated satellite-terrestrial networks, in which the satellite can utilize the ISAC signal to sense the malicious eavesdropper with an uncertain location while offloading data with improved secrecy rates. To investigate this problem, we formulate a joint optimization of the transmit beamforming, the receive beamforming, the computation offloading strategies and the associated allocations of the communication and computing resources, with the objective of maximizing the minimum sensing performance for all possible eavesdropper locations, while guaranteeing the secrecy offloading transmission rate. Despite the nonconvexity of the formulated problem, we propose an efficient algorithm to obtain its solutions. Numerical results validate the performance advantages of our ISAC empowered secure computation offloading in secrecy and robustness.