I leave it as a simple exercise for the reader to convert this solution from commandline to pgmagick (see more below). The code underlying pgmagick is the same as that used by the commandline.
You could draw the circle larger and then "resize" it down. This ameliorates the jaggy look of the circle by averaging the edge with the surrounding background during the resizing operation.
Instead of
gm convert -size 220x220 xc:none -fill white \
-draw "circle 110,110, 33.75,33.75" \
original.png
Do this:
gm convert -size 880x880 xc:none -fill white \
-draw "circle 440,440, 135,135" \
-resize 25% resized.png
You could try other sizes and decide which is the smallest that satisfies you, e.g.,
gm convert -size 440x440 xc:none -fill white \
-draw "circle 220,220, 67.5,65.5" \
-resize 50% resized.png
This commandline works on both GraphicsMagick ("gm convert") and ImageMagick ("convert")
Looking at the pgmagick documentation at http://pgmagick.readthedocs.org/en/latest/cookbook.html#scaling-a-image it is not clear that pgmagick offers "resize". The documentation shows "img.scale" which will probably result in a jaggy circle. Using "-scale" on the commandline examples above instead of "-resize" does indeed produce the same jaggy image.
pgmagick does however allow you to specify the filter type, as in
img.scale((150, 100), 'lanczos')
which should be equivalent to "-resize" and is what you want.