While scene text image super-resolution (STISR) has yielded remarkable improvements in accurately recognizing scene text, prior methodologies have placed excessive emphasis on optimizing performance, rather than paying due attention to efficiency - a crucial factor in ensuring deployment of the STISR-STR pipeline. In this work, we propose a novel Efficient Scene Text Image Super-resolution (ESTISR) Network for resource-limited deployment platform. ESTISR's functionality primarily depends on two critical components: a CNN-based feature extractor and an efficient self-attention mechanism used for decoding low-resolution images. We designed a re-parameterized inverted residual block specifically suited for resource-limited circumstances as the feature extractor. Meanwhile, we proposed a novel self-attention mechanism, softmax shrinking, based on a kernel-based approach. This innovative technique offers linear complexity while also naturally incorporating discriminating low-level features into the self-attention structure. Extensive experiments on TextZoom show that ESTISR retains a high image restoration quality and improved STR accuracy of low-resolution images. Furthermore, ESTISR consistently outperforms current methods in terms of actual running time and peak memory consumption, while achieving a better trade-off between performance and efficiency.