Well, you could do it in Photoshop; but I wouldn't. Better to do it on paper in the first place; than to have your computer mush up your letterforms afterwards... Draw a circle lightly on the paper with a pencil, and use that as your baseline, when drawing out the calligraphy...

 I suppose I'll do that next time. For now, though, I was intending to warp the image on the computer and then retrace the calligraphy once it's in hemicircular form. (Then I was planning to go crazy and blow the image up by 2× and edit the fine detail with marker, pen, and white-out…)
 Also, and this is not obvious from the low-res scan I've posted below, I'm using a graph paper grid to help me space and position things. In order to redraw this on a half-circle, I need some sort of circular graph paper with the same spacings as what I've built my lettering around. And then there's the next line of text that I'm intending to put on a bit of a wave.
 Any suggestions?
—Joel

> how can I achieve this twisting with a scanned image?

With work :)

Photoshop: Transform -> Wrap , or Perspective

1. sketch the curved typography roughly how you'd like it.
2. map it onto a circle grid as desired. you should make one for yourself.
3. use the pshop polar coordinates distortion filter to remap the sketch
-from polar to rectangular.
4. draw the type cleanly using the new rectangular distortion as a guide.
5. reverse the distortion back to polar using pshop filter.
6. clean up as needed.