Let $G(n,m)$ be a simple graph with vertex set $V$ and $S\subseteq V$ with $|S|=\sigma.$ The graph $G_S$ is obtained by adding a self-loop to each vertex of the graph $G$ in the set $S$. The Randić index of a graph is one of the important topological indices which has its application in chemistry. In this manuscript, the Randić index of a graph with self-loops is defined and are obtained some bounds for the same.