The combined use of ultrasound radiation and microfluidics is a promising tool for aiding the development of lab-on-a-chip devices. In this study, we show that the rotation of linear aggregates of micro-particles can be achieved under the action of acoustic field pressure. This novel manipulation is investigated by tracking polystyrene beads of different sizes through the 3D imaging features of digital holography (DH). From our analysis it is understood that the positioning of the micro-particles and their aggregations are associated with the effect of bulk acoustic radiation forces. The observed rotation is instead found to be compatible with the presence of acoustic streaming patterns as evidenced by our modelling and the resulting numerical simulation. Furthermore, the rotation frequency is shown to depend on the input voltage applied on the acoustic device. Finally, we demonstrate that we can take full advantage of such rotation by combining it with quantitative phase imaging of DH for a significant lab-on-a-chip biomedical application. In fact, we demonstrate that it is possible to put in rotation a linear aggregate of erythrocytes and rely on holographic imaging to achieve a full phase-contrast tomography of the aforementioned aggregate.