With the growing demand for satellite sensing and communication, the limited wireless resources are difficult to support multiple satellite systems. Therefore, it is desired to investigate integrated sensing and communication (ISAC) in low Earth orbit (LEO) satellite systems to enable multifunctionality within a single satellite, thereby saving both spectrum and orbital resources. In this article, a framework for ISAC in LEO satellite systems is established, where a satellite can simultaneously sense multiple targets and serve multiple communication users (CUs) over the same spectrum. Considering the limited onboard energy of the satellite, a novel robust beamforming design algorithm is developed with the goal of minimizing total transmit power while satisfying the mean squared error (mse) requirements for sensing and signal-to-interference-plus-noise ratio (SINR) requirements for communication in the presence of channel phase uncertainty, which exacerbates the cross-functional interference. According to theoretical analysis, the proposed algorithm for ISAC in LEO satellite systems is effective. Moreover, extensive simulations confirm the superiority of the proposed algorithm over baselines.