  Let $K_n$ denote the complete graph on $n$ vertices and $G, H$ be finite
graphs. Consider a two-coloring of edges of $K_n$. When a copy of $G$ in the
first color, red, or a copy of $H$ in the second color, blue is in $K_n$, we
write $K_n\rightarrow (G,H)$. The Ramsey number $r(G, H)$ is defined as the
smallest positive integer $n$ such that $K_{n} \rightarrow (G, H)$. Star
critical Ramsey $r_*(G, H)$ is defined as the largest value of $k$ such that
$K_{r(G,H)-1} \sqcup K_{1,k} \rightarrow (G, H)$. In this paper, we find
$r_*(C_n, K_m)$ for $m \geq 7$ and $n \geq (m-3)(m-1)$.
