In attempts to engineer human tissues in the lab, bio-mimicking the cellular arrangement of natural tissues is critical to achieve the required biological and mechanical form and function. Although biofabrication employing cellular bioinks continues to evolve as a promising solution over polymer scaffold based techniques in creating complex multi-cellular tissues, the ability of most current biofabrication processes to mimic the requisite cellular arrangement is limited. In this study, we propose a novel biofabrication approach that uses forces generated by bulk standing acoustic waves (BSAW) to non-deleteriously align cells within viscous bioinks. We computationally determine the acoustic pressure pattern generated by BSAW and experimentally map the effects of BSAW frequency (0.71, 1, 1.5, 2 MHz) on the linear arrangement of two types of human cells (adipose-derived stem cells and MG63) in alginate. Computational results indicate a non-linear relationship between frequency and acoustic pressure amplitude. Experimental results demonstrate that the spacing between adjacent strands of aligned cells is affected by frequency (p < 0.0001), and this effect is independent of the cell type. Lastly, we demonstrate a synergistic technique of gradual crosslinking in tandem with the BSAW-induced alignment to entrap cells within crosslinked hydrogels. This study represents an advancement in engineered tissue biofabrication aimed at bio-mimicry.