Hi. There are a few ways to do this.
One way to do this is to use my “Separate_Masks_in_Layers” script. It has a feature which calculates centers based on the masks you give it. So you could theoretically put a mask which matches the circle on the image, then run the script on the layer and let it calculate the center based on the mask. One caveat, though: It won’t run if there is only one mask on a layer, so you could do [Layer>Mask>New Mask] first, making a mask for the whole thing, then make your circular mask (using the Ellipse Tool, perhaps) and run the script, afterward deleting both the “main mask layer”, and the circular mask in the remaining layer.
My ReAnchor_Selected_Layers script is for placing single-vertex-masks quickly on layers on which it is easy or perhaps not-so-crucial as far as where the new anchor points go. “Eyeballing” this kind of thing can be frustrating, because you cannot, for example, free-transform a mask and move guides to the center of the mask (which becomes visible when free-transforming); the two things — free transforming a mask, and dragging a guide to where you want — cannot happen at the same time. You can zoom way the heck in, though, and try to find the exact pixel on which to pop a singe-vertex-mask, then run the ReAnchor script.
https://www.crgreen.com/aescripts/