Controlled intracellular delivery of biomolecular cargo is critical for developing targeted therapeutics and cell reprogramming. Conventional delivery approaches (e.g., endocytosis of nano-vectors, microinjection, and electroporation) usually require time-consuming uptake processes, labor-intensive operations, and/or costly specialized equipment. Here, we present an acoustofluidics-based intracellular delivery approach capable of effectively delivering various functional nanomaterials to multiple cell types (e.g., adherent and suspension cancer cells). By tuning the standing acoustic waves in a glass capillary, our approach can push cells in flow to the capillary wall and enhance membrane permeability by increasing membrane stress to deform cells via acoustic radiation forces. Moreover, by coating the capillary with cargo-encapsulated nanoparticles, our approach can achieve controllable cell-nanoparticle contact and facilitate nanomaterial delivery beyond Brownian movement. Based on these mechanisms, we have successfully delivered nanoparticles loaded with small molecules or protein-based cargo to U937 and HeLa cells. Our results demonstrate enhanced delivery efficiency compared to attempts made without the use of acoustofluidics. Moreover, compared to conventional sonoporation methods, our approach does not require special contrast agents with microbubbles. This acoustofluidics-based approach creates exciting opportunities to achieve controllable intracellular delivery of various biomolecular cargoes to diverse cell types for potential therapeutic applications and biophysical studies.