Scale-freeness is a common phenomenon often observed in complex systems poised at critical states, where there is no characteristic scale that governs the whole systems. Scale-free correlations have been found in bird flocks and brain tumor cells, indicating a common result of collective motion of coordinated agents. This paper concerns scale-free correlations of the orientational order of two-dimensional polygonal cells arranged in a disordered hyperuniform way, where the centroids of cells are more or less equi-distanced from each other. The hyperuniform state is achieved by using a geometric algorithm, called Lloyd's algorithm, along the iterations of which non-hexagonal topological defects emerge to create strand-like structures embedded in otherwise a hexagonal domain.