Protein linkages to filamentous (F)-actin provide the cell membrane with mechanical resiliency and give rise to intricate membrane architectures. However, the actin cytoskeleton is highly dynamic, and undergoes rapid changes in shape during cell motility and other processes. The molecular mechanisms that underlie the mechanically robust yet fluid connection between the membrane and actin cytoskeleton remain poorly understood. Here, we used a single-molecule optical trap assay to examine how the prototypical membrane-actin linker ezrin acts to anchor F-actin to the cell membrane. Remarkably, we find that ezrin forms a complex that slides along F-actin over micron distances while resisting mechanical detachment. The ubiquity of ezrin and analogous proteins suggests that sliding anchors such as ezrin may constitute an important but overlooked element in the construction of the actin cytoskeleton.