In this paper, following the concept of $A^\mathcal {I}$-statistical convergence for real sequences introduced by Savas et al. \cite{espdsd2}, we deal with Korovkin type approximation theory for a sequence of positive convolution operators defined on $C[a,b]$, the space of all real valued continuous functions on $[a,b]$, in the line of Duman \cite{duman3}. In the Section 3, we study the rate of $A^\mathcal {I}$-statistical convergence.