Significance We present 3D acoustic tweezers, which can trap and manipulate single cells and particles along three mutually orthogonal axes of motion by recourse to surface acoustic waves. We use 3D acoustic tweezers to pick up single cells, or entire cell assemblies, and deliver them to desired locations to create 2D and 3D cell patterns, or print the cells into complex shapes. This technology is thus shown to offer better performance over prior cell manipulation techniques in terms of both accurate and precise motion in a noninvasive, label-free, and contactless manner. This method offers the potential to accurately print 3D multicellular architectures for applications in biomanufacturing, tissue engineering, regenerative medicine, neuroscience, and cancer metastasis research.