In this paper, we present the theoretical background, design, fabrication and characterization of a micromachined chamber assisting the fluidic self-assembly of micro-electro-mechanical systems in a bulk liquid. Exploiting bubble-induced acoustic microstreaming, several structurally-robust driving modes are excited inside the chamber. The modes promote the controlled aggregation and disaggregation of microcomponents relying on strong and reproducible fluid mixing effects achieved even at low Reynolds numbers. The functionality of the microfluidic chamber is demonstrated through the fast and repeatable geometrical pairing and subsequent unpairing of polymeric microcylinders. Relying only on drag and radiation forces and on the natural hydrophobicity of SU-8 in aqueous solutions, assembly yields of approximately 50% are achieved in no longer than ten seconds of agitation. The system can stochastically control the assembly process and significantly reduce the time-to-assembly of building blocks.