The Koebe-Andreev-Thurston theorem states that for any triangulation of a closed orientable surface $\Sigma_g$ of genus $g$ which is covered by a simple graph in the universal cover, there exists a unique metric of curvature $1, 0$ or $-1$ on the surface depending on whether $g=0, 1$ or $ \ge 2$ such that the surface with this metric admits a circle packing with combinatorics given by the triangulation. Furthermore, the circle packing is essentially rigid, that is, unique up to conformal automorphisms of the surface isotopic to the identity.\\ \hspace*{3mm} In this paper, we consider projective structures on the surface where circle packings are also defined. We show that the space of projective structures on a surface of genus $g \geq 2$ which admits a circle packing contains a neigborhood of the Koebe-Andreev-Thurston structure homeomorphic to $\mathbb{R}^{6g-6}$. We furthemore show that if a circle packing consists of one circle, then the space is globally homeomorphic to $\mathbb{R}^{6g-6}$ and that the circle packing is rigid.