We develop a finite element method with continuous displacements and discontinuous rotations for the Reissner-Mindlin plate model on quadrilateral elements. To avoid shear locking, the rotations must have the same polynomial degree in the parametric reference plane as the parametric derivatives of the displacements, and obey the same transforma- tion law to the physical plane as the gradient of displacements. We prove optimal conver- gence, uniformly in the plate thickness, and provide numerical results that confirm our estimates.