We know the radius of the circle is $OA = \sqrt{(A_x-O_x)^2 + (A_y-O_y)^2}$. We can also find $AB = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$. Since we know $OA$, $OB$ (which is simply $OA$) and $AB$, we can find $\angle AOB$ using the Cosine Rule. Once we have $\angle OAB$, then the arc length $ACB$ is equal to:
$$ \frac{\angle AOB}{360^{\circ}} \cdot 2\pi \cdot OA $$
EDIT:
To obtain $\angle AOB$, we know that by Cosine Rule:
$$ cos \angle AOB = \frac{AB^2 - OA^2 - OB^2}{2} $$
Thus $\angle AOB = cos^{-1}(\frac{AB^2 - OA^2 - OB^2}{2})$