In this paper we consider the notion of $A^\cal {I}_2$-statistical convergence for real double sequences which is an extension of the notion of $A^\cal {I}$-statistical convergence for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of $A^\cal {I}_2$-statistical convergence.