The only way I know of to get a smooth edge on a bitmap graphic is with the eraser tool, but you must have a steady hand and a lot of patients. If you do not have the patients and a steady hand, the next best thing for smoothing a bitmap graphic is feathering the edge, but it is not as smooth as the eraser as you will see if you try each and compare. Also, feathering makes the edge blurry, and the smoother the edge the blurrier it becomes, so it's a trade off.
What I would use if I wanted to make a smooth circle in PS is a vector graphic, which the custom shapes are. (The pen tool also draws in vector format.) I would choose the thin circle in the custom shapes palette, then drag out a perfect circle. You will see that the edge of this circle actually is comprised of two circles, one slightly smaller and inside the other, so you can simply fill the interior if you want a solid color circle. To do this I rasterize the shape, then ctrl+click the custom shape's layer in the layers palette, then edit/fill with white (or what ever color you want). Then click in the center of the shape with the magic wand. Then I edit/transform/scale. Then I click the link icon in between the percentage windows near the top of the screen, and highlight the 100% in one of the windows (doesn't matter which because you've clicked the link icon to make both H and V proportions change equally), I then would type in the number 106 (106%) and this will grow the selection the wand has made to the center of the two circles on an 80px by 80px circle, which this is. Then you simply edit/fill with white (or whatever color you want). select/de-select and, voila.
The vector graphic (custom shape) is the one marked CS. The others are bitmap graphics feathered with .2, .5, 1 feather tolerances, and the one marked E is the same as 1 but with a perimiter selection that I added and quickly erased around. That just made it a bit crisper and a little less blurry.
But as you can see, vector is the way to go for smoothness. And BTW, vector is also resolution independent, so it sizes without pixel distortion. (note: vector is what format Adobe Illustrator draws in if you have AI).
Vector format is really what your avatar should have been created in, mainly because it is white (is highly contrasted against a dark background), and because it is a circle (the shape that shows the most bitmap irregularity).