Let the center of the circle be $ (x,0) $. Then we know the distance from the center to $ (-3,2) $ and from the center to $ (-2,3) $ are the same. Using the distance formula, we have \begin{align*} \sqrt{(x+3)^2+(0-2)^2}&=\sqrt{(x+2)^2+(0-3)^2}\\ \Rightarrow\qquad \sqrt{x^2+6x+9+4}&=\sqrt{x^2+4x+4+9}\\ \Rightarrow\qquad 6x&=4x\\ \Rightarrow\qquad x&=0\\ \end{align*}Now we know the center of the circle is $ (0,0) $, and we need to find the radius. Use the distance formula once more: $$\sqrt{(0+3)^2+(0-2)^2}=\sqrt{3^2+(-2)^2}=\sqrt{9+4}=\boxed{\sqrt{13}}.$$