Use the elliptical select tool, hold down CTRL key to constrain as square, fill the selected area with new color, right click on selected area, choose SELECT, SHRINK, shrink selection by whatever number of pixels you want your circle width to be, right click again in selected area, choose EDIT, CUT. Voila, one beautifully antialased square.
Photoshop is also use this method in the old version,although it can directly draw a circle or a square,its look&fell is no AAer than the method above...This is the STANDARD method.