If before 'arc'ing an image you rotate the input image upside-down, you can place the original 'top' of the image on the inside edge of the circle. Of course you may like to 'rotate' the result back upright again afterward, but that capability is already built into the 'Arc' distortion method.
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convert -font Candice -pointsize 20 label:' Around the World ' -virtual-pixel Background -background SkyBlue -rotate 180 -distort Arc '270 180' arc_flip.jpg
I am running the command through Windows' command prompt. I had to change certain characters of the code sample (apparently single ticks are not interchangeable with double-quotes on Windows) and alter the font, but I am able to run the command:
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"C:\Program Files\ImageMagick-7.0.2-Q16\convert.exe" -font Arial -pointsize 20 label:"Around the World" -virtual-pixel Background -background SkyBlue -rotate 180 -distort Arc "270 180" arc_flip.png
Any ideas on what I am doing wrong?
[edit] Here's my convert.exe -version log:
C:\temp>"C:\Program Files\ImageMagick-7.0.2-Q16\convert.exe" -version
Version: ImageMagick 7.0.2-7 Q16 x64 2016-08-06 http://www.imagemagick.org
Copyright: Copyright (C) 1999-2015 ImageMagick Studio LLC
License: http://www.imagemagick.org/script/license.php
Visual C++: 180040629
Features: Cipher DPC Modules OpenMP
Delegates (built-in): bzlib cairo flif freetype jng jp2 jpeg lcms lqr openexr pangocairo png ps rsvg tiff webp xml zlib