We numerically investigate the effects of a density-dependent gauge potential which induces nonlinear rotation in a Bose-Einstein condensate confined in a toroidal trapping geometry. By focusing on the resulting vortex lattice configurations, we demonstrate that increasing the strength of the nonlinear rotation leads to a structural transition from a ring-shaped vortex lattice to a giant vortex state. The quantum circulation associated with the giant vortex is found to be highly sensitive to the strength of the nonlinear rotation and the giant vortex appears in the regime of negative chemical potential. Positive nonlinear rotation modifies the effective nonlinear response of the condensate through a density-dependent rotational contribution that competes with the repulsive contact interaction ($g>0$), thereby influencing the structural transition from a ring-shaped vortex lattice to a giant-vortex state. Additionally, we identify the parameter regime in which the Thomas-Fermi density profile remains valid by mapping the solution space based on the strength of the nonlinear rotation and the radius of the confining potential. Based on the Bogoliubov de Gennes analysis, we investigate the impact of nonlinear rotation on the collective excitation spectrum. Our results reveal modifications in the collective-mode frequencies, particularly the breathing mode, associated with the radial deformation of the condensate in the toroidal geometry. Our findings are further substantiated through a comprehensive hydrodynamic analysis. Finally, we analyze the stability of multiply quantized vortices under nonlinear rotation. Our findings indicate that while nonlinear rotation can enhance the global stability of these states, it does not necessarily ensure their local stability.