Cellulose nanocrystals (CNCs) have received attention as a biological alternative for the stabilization of fluid interfaces, yielding biocompatible and sustainable emulsions, foams, and aerogels. The interfacial behavior of nanoparticles with shape anisotropy and surface charge like CNCs is still poorly understood, although it ultimately dictates the mechanical properties and stability of the macroscopic colloidal material. Here, we report on the linear and nonlinear interfacial dilatational and shear rheology of CNCs at the air water interface. We observed the formation of viscoelastic CNC layers at comparably low surface coverage, which was attributed to the shape anisotropy of CNCs. Further, the interfacial elasticity of CNC layers can be modulated by salt-induced charge screening, thereby shifting the interplay of repulsive and attractive CNC interactions. CNC layers had a viscous character without salt, followed by increasing viscoelasticity upon salt addition. CNC layers display strain hardening during compression and show a yield stress followed by flow under shear. The observed interfacial behavior is discussed in the context of CNC-stabilized foam and emulsion properties. We conclude that understanding the CNC interfacial behavior may help improve the performance of CNC-stabilized colloidal materials.