Selective actuation of a single microswimmer from within a diverse group would be a first step toward collaborative guided action by a group of swimmers. Here we describe a new class of microswimmer that accomplishes this goal. Our swimmer design overcomes the commonly-held design paradigm that microswimmers must use non-reciprocal motion to achieve propulsion; instead, the swimmer is propelled by oscillatory motion of an air bubble trapped within the swimmer's polymer body. This oscillatory motion is driven by the application of a low-power acoustic field, which is biocompatible with biological samples and with the ambient liquid. This acoustically-powered microswimmer accomplishes controllable and rapid translational and rotational motion, even in highly viscous liquids (with viscosity 6,000 times higher than that of water). And by using a group of swimmers each with a unique bubble size (and resulting unique resonance frequencies), selective actuation of a single swimmer from among the group can be readily achieved.