Deep learning has achieved significant success in hyperspectral image super-resolution (HSISR) by leveraging advanced feature extraction techniques to reconstruct high-resolution images from low-resolution counterparts. However, existing methods predominantly utilize 2D/3D convolutions or Transformer architectures, which are often hindered by limited receptive fields, quadratic computational complexity, and inadequate fusion of spatial-spectral dependencies. To address these challenges, this paper proposes RWKVSR, a novel lightweight network that integrates a Receptance Weighted Key-Value (RWKV) architecture for efficient HSISR. The proposed RWKVSR comprises of three key components: (1) A linear-complexity RWKV module replacing quadratic self-attention, enabling efficient global spectral-spatial modeling; (2) A Spectral-Spatial Residual Module (SSRM) employing anisotropic, direction-separable 3D convolutions to hierarchically extract multi-scale features while enhancing local-global interactions; and (3) A Hyperspectral Frequency Loss (HFL) optimizing spectral consistency by prioritizing high-frequency structural alignment between reconstructed and ground-truth images in the frequency domain. Extensive experiments conducted on the CAVE and Harvard datasets demonstrate that RWKVSR outperforms the existing state-of-the-art methods, effectively balancing accuracy and efficiency, and providing a practical solution for high-quality HSI reconstruction.