I'm not sure if this is a true statement, but I suspect that best way to do it is to upload the map to an image hosting site (Google "image hosting" if you don't have your own server). If you've got a blog, you could also post it as a part of a blog post (I believe Blogger lets you do this), maybe an article about Geocaching, or whatnot.
Once you have it uploaded, you'll need to find the URL. If it isn't obvious from the site what the URL is (i.e., if the image hosting site doesn't tell you "to access this file, use the following HTML code"), get to the point where you can see it. For example, if you've uploaded it into a Blogspot blog, look at your blog. Then use the View pull-down menu and select "View Source". Find the reference to the graphic -- it'll look something like this:
<img border=0 src="http://file_location/your-graphic-filename.ext" alt="alternate text">
Note that it won't actually say "file_location"; it'll be the actual WWW location of your file. Copy this <img> tag and then paste it into your Profile Details.
I am sure there are some other ways to get pictures up into geocaching.com. I know that when you upload a picture that's part of one of your logs, it goes into your gallery, and then could be called (again, pull up the source of the gallery page to find the <img> tag to copy). However, I haven't figured out whether you can create a log that's not actually a part of a cache or trackable log (and I don't imagine it's a good idea at all to simply upload a map graphic to a cache log -- one that's not related to the cache at all -- just for the purpose of getting it online so that you can link to it. Wouldn't recommend that at all). Hopefully someone will be able to tell you if that's possible.
P.S. The "alt" text that's part of the <img> tag, above, is what pops up when people let their mouse cursors "linger" on your image. It is also what is read by software used for the visually impared. I always recommend putting some content in here for that reason.
I hope this helps!