With the rapid development of diffusion models, style transfer has made remarkable progress. However, flexible and localized style editing for scene text remains an unsolved challenge. Although existing scene text editing methods have achieved text region editing, they are typically limited to content replacement and simple styles, which lack the ability of free-style transfer. In this paper, we introduce SceneTextStylizer, a novel training-free diffusion-based framework for flexible and high-fidelity style transfer of text in scene images. Unlike prior approaches that either perform global style transfer or focus solely on textual content modification, our method enables prompt-guided style transformation specifically for text regions, while preserving both text readability and stylistic consistency. To achieve this, we design a feature injection module that leverages diffusion model inversion and self-attention to transfer style features effectively. Additionally, a region control mechanism is introduced by applying a distance-based changing mask at each denoising step, enabling precise spatial control. To further enhance visual quality, we incorporate a style enhancement module based on the Fourier transform to reinforce stylistic richness. Extensive experiments demonstrate that our method achieves superior performance in scene text style transformation, outperforming existing state-of-the-art methods in both visual fidelity and text preservation.