I had to use mp3 instead of wav, but all i did was connect my phone as USB storage. Then you navigate to media/audio/ringtones ( if you have it). If you dont have it just create that folder structure and place your mp3s in the ringtones folder.
If you wanna do it without a computer just use Astro or Estrong to copy the files. Once you download them through Dropbox, just copy them to the right folder. No root necessary.
They will then show up in settings, sound, phone ringtone menu.
I actually have the same problem with putting pictures in my dropbox. I download them but they won't show up in my gallery. I know they're there because I can browse to them in root explorer and open them from there.
No clue why, though
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When you download them, it saves them to /sdcard/Dropbox/Photos/whatevername
This is apparently too deep a folder structure for Gallery to look so it doesn't find the pictures. When they are moved to the top Dropbox folder it finds them.