Try to prove a surface is ruled

Question

Suppose that $X$ is a projective smooth surface. And $C$ is a irreducible curve on $X$ s.t. $C\simeq \mathbb{P}^1$ and $(C^2)=0$. Can we prove that there exists a morphism $\phi: X\rightarrow Y$ to a smooth projective curve such that $\phi_*O_X=O_Y$