Integrated sensing and communication (ISAC) is an encouraging wireless technology which can simultaneously perform both radar and communication functionalities by sharing the same transmit waveform, spectral resource, and hardware platform. Recently emerged symbol-level precoding (SLP) technique exhibits advancement in ISAC systems by leveraging the waveform design degrees of freedom (DoFs) in both temporal and spatial domains. However, traditional SLP-based ISAC systems are designed in a modular paradigm, which potentially limits the overall performance of communication and radar sensing. The high complexity of existing SLP design algorithms is another issue that hurdles the practical deployment. To break through the bottleneck of these approaches, in this paper we propose an end-to-end approach to jointly design the SLP-based dual-functional transmitter and receivers of communication and radar sensing. In particular, we aim to utilize deep learning-based methods to minimize the symbol error rate (SER) of communication users, maximize the detection probability, and minimize the root mean square error (RMSE) of the target angle estimation. Multi-layer perceptron (MLP) networks and a long short term memory (LSTM) network are respectively applied to the transmitter, communication users and radar receiver. Simulation results verify the feasibility of the proposed deep-learning-based end-to-end optimization for ISAC systems and reveal the effectiveness of the proposed neural networks for the end-to-end design.