It is critical to design efficient beamforming in reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) systems for enhancing spectrum utilization. However, conventional methods often have limitations, either incurring high computational complexity due to iterative algorithms or sacrificing performance when using heuristic methods. To achieve both low complexity and high spectrum efficiency, an unsupervised learning-based beamforming design is proposed in this work. We tailor image-shaped channel samples and develop an ISAC beamforming neural network (IBF-Net) model for beamforming. By leveraging unsupervised learning, the loss function incorporates key performance metrics like sensing and communication channel correlation and sensing channel gain, eliminating the need of labeling. Simulations show that the proposed method achieves competitive performance compared to benchmarks while significantly reduces computational complexity.