This study investigates the universal I-Love-Q relation in anisotropic quark stars within the Rastall gravity framework. We employ the 4th-order Runge-Kutta numerical method to solve the slow rotation and tidal deformation equations. The analysis utilizes the MIT Bag equation of state with the Bag parameter () and the Color Flavor Locked (CFL) equation of state with the CFL parameter parameter () to model the material properties of anisotropic quark stars. The universal I-Love-Q relation are explored by varying the Rastall parameter () and the anisotropic parameter (). The universal I-Love-Q relation is satisfied when variations in  , , , and do not affect the linear relationship between the moment of inertia (), Love number (), and quadrupole moment (). The universal I-Love-Q relation holds when  and  are varied , but breaks down when ζ and  are altered.