Hello, title says it all.

Is there a way to make the cursor stay as a circle, and not become a square, when it is as small as 3 pixels?

Thank you!

Do you mean the cursor or the brush outline?
The 'small circle' cursor is always a small circle. The brush outline is the best it can be at 3px because of the limitations of using a pixel grid (raster) representation of an image (and a brush stroke).
If I've misunderstood what's happening here, please post an image to illustrate what you mean.