The alignment of anisotropic particles during ink deposition directly affects the microstructure and properties of materials manufactured by extrusion-based 3D printing. Although particle alignment in diluted suspensions is well described by analytical and numerical models, the dynamics of particle orientation in the highly concentrated inks typically used for printing via direct ink writing (DIW) remains poorly understood. Using cellulose nanocrystals (CNCs) as model building blocks of increasing technological relevance, we study the dynamics of particle alignment under the shear stresses applied to concentrated inks during DIW. With the help of in situ polarization rheology, we find that the time period needed for particle alignment scales inversely with the applied shear rate and directly with the particle concentration. Such dependences can be quantitatively described by a simple scaling relation and qualitatively interpreted in terms of steric and hydrodynamic interactions between particles at high shear rates and particle concentrations. Our understanding of the alignment dynamics is then utilized to estimate the effect of shear stresses on the orientation of particles during the printing process. Finally, proof-of-concept experiments show that the combination of shear and extensional flow in 3D printing nozzles of different geometries provides an effective means to tune the orientation of CNCs from fully aligned to core–shell architectures. These findings offer powerful quantitative guidelines for the digital manufacturing of composite materials with programmed particle orientations and properties.