The motility of microorganisms is often biased by gradients in physical and chemical properties of their environment, with myriad implications on their ecology. Here we show that fluid acceleration reorients gyrotactic plankton, triggering small-scale clustering. We experimentally demonstrate this phenomenon by studying the distribution of the phytoplankton Chlamydomonas augustae within a rotating tank and find it to be in good agreement with a new, generalized model of gyrotaxis. When this model is implemented in a direct numerical simulation of turbulent flow, we find that fluid acceleration generates multifractal plankton clustering, with faster and more stable cells producing stronger clustering. By producing accumulations in high-vorticity regions, this process is fundamentally different from clustering by gravitational acceleration, expanding the range of mechanisms by which turbulent flows can impact the spatial distribution of active suspensions.