Scene Text Image Super-Resolution (STISR) aims to enhance the resolution and legibility of text within low-resolution (LR) images, consequently elevating recognition accuracy in Scene Text Recognition (STR). Previous methods predominantly employ discriminative Convolutional Neural Networks (CNNs) augmented with diverse forms of text guidance to address this issue. Nevertheless, they remain deficient when confronted with severely blurred images, due to their insufficient generation capability when little structural or semantic information can be extracted from original images. Therefore, we introduce RGDiffSR, a Recognition-Guided Diffusion model for scene text image Super-Resolution, which exhibits great generative diversity and fidelity even in challenging scenarios. Moreover, we propose a Recognition-Guided Denoising Network, to guide the diffusion model generating LR-consistent results through succinct semantic guidance. Experiments on the TextZoom dataset demonstrate the superiority of RGDiffSR over prior state-of-the-art methods in both text recognition accuracy and image fidelity.