In the present paper, we study on the subclass of starlike functions of complex order with bounded radius rotation using $q-$ difference operator denoted by $\mathcal{R}_{k}(q, b)$ where $k\geq2$, $q\in(0,1)$ and $b\in\mathbb{C}\backslash \{0\}$. We investigate coefficient inequality, distortion theorem and radius of starlikeness for the class $\mathcal{R}_{k}(q, b)$.