360-degree video offers users an immersive viewing experience by enabling them to look around during playback. However, this type of video consumes a significant amount of data, necessitating high bandwidth and minimal streaming delays. Super-Resolution (SR) is an emerging technique that can enhance video quality while reducing data transmission requirements. It achieves this by sending low-quality video and utilizing an SR model on the client side to enhance its quality. Nonetheless, SR is computationally demanding and typically requires high-performance hardware, making it impractical for many weak clients, particularly mobile devices. To overcome this limitation, we propose EdgeSR, an edge-assisted approach that combines rate adaptation and quality enhancement for 360-degree video streaming. In EdgeSR, the client can request low-quality video chunks from the cloud and perform SR at the edge to enhance video quality while minimizing transmission delays from the cloud to the edge. Simultaneously, the edge node can prefetch a video chunk from the cloud while the previous one is being transmitted from the edge to the client, thereby reducing delays. Experimental results under various settings demonstrate that EdgeSR outperforms the most competitive baseline methods, improving the overall Quality of Experience (QoE) by 27%.