Hello StickJump!
Let's premise this with the fact that a new curve editor is under work right now, which will allow separate x and y curves, making it easier to get that perfect circular or elliptical motion.
There are other ways besides using paths to get circular motions easily.
The easiest in my opinion is to parent the bone you want to move into a circular motion to another bone. Disable inherit rotation on the child bone, and rotate the parent bone. The parent bone will act as pivot of the rotation, and how far the child bone is from the parent determines the width of the circle.
If you want elliptical motion add a bone as parent that will scale non-uniformly the children, getting an elliptical rotation. You can disable inherit scale on the child bone. Just like the windmill blades in this example:
Windmill example: Windmill Blades
Another way is to move the parent bone vertically and apply easing in the graph, while moving the child bone horizontally. Offset the child bone and you get the circular motion!
Here's how the 3 examples look like:

And here's a downloadable project:
rotations.spine
Related topics:
Dopesheet - Spine User Guide: Key Offset
Graph - Spine User Guide