Arrowrat.
Have a read of this page on the old Follow the Arrow website (now hosted by GAGB). If you scroll down the page, it will tell you about Adding images to a page.
http://follow-the-arrow.gagb.org.uk/htmlcodes.html
As long as the image is uploaded somewhere onto the Groundspeak (Geocaching.com) website - either in a log or content of a cache page / archived cache, then you will be able to link to it and add a 'badge/image' to your profile page. You can host the image elsewhere (like the PhotoBucket), but it's easier just to keep on the Geocaching.com website.
GAGB member since 2005
GAGB Committee member 2010 to 2016 (Chair 2012 to 2015)
UK Mega Event Chairman 2009 (Weston-super-Mare)