Text-to-image (T2I) diffusion models (DMs) have shown promise in generating high-quality images from textual descriptions. The real-world applications of these models require particular attention to their safety and fidelity, but this has not been sufficiently explored. One fundamental question is whether existing T2I DMs are robust against variations over input texts. To answer it, this work provides the first robustness evaluation of T2I DMs against real-world attacks. Unlike prior studies that focus on malicious attacks involving apocryphal alterations to the input texts, we consider an attack space spanned by realistic errors (e.g., typo, glyph, phonetic) that humans can make, to ensure semantic consistency. Given the inherent randomness of the generation process, we develop novel distribution-based attack objectives to mislead T2I DMs. We perform attacks in a black-box manner without any knowledge of the model. Extensive experiments demonstrate the effectiveness of our method for attacking popular T2I DMs and simultaneously reveal their non-trivial robustness issues. Moreover, we provide an in-depth analysis of our method to show that it is not designed to attack the text encoder in T2I DMs solely.