The growth of actin filament networks is a fundamental biological process that drives a variety of cellular and intracellular motions. During motility, eukaryotic cells and intracellular pathogens are propelled by actin networks organized by nucleation-promoting factors that trigger the formation of nascent filaments off the side of existing filaments in the network. A Brownian ratchet (BR) mechanism has been proposed to couple actin polymerization to cellular movements, whereby thermal motions are rectified by the addition of actin monomers at the end of growing filaments. Here, by following actin-propelled microspheres using three-dimensional laser tracking, we find that beads adhered to the growing network move via an object-fluctuating BR. Velocity varies with the amplitude of thermal fluctuation and inversely with viscosity as predicted for a BR. In addition, motion is saltatory with a broad distribution of step sizes that is correlated in time. These data point to a model in which thermal fluctuations of the microsphere or entire actin network, and not individual filaments, govern motility. This conclusion is supported by Monte Carlo simulations of an adhesion-based BR and suggests an important role for membrane tension in the control of actin-based cellular protrusions.