In earlier days of the internet, before HTML 3.2, the tilde character (~) was explicitly NOT allowed in a url. It had to be encoded as %7e. This restriction was later relaxed, and Google will index a url that contains a tilde.
It's been quite a few years since the absolute prohibition on using tilde in a url was relaxed, and standardization has moved ahead rapidly. But it's still a bad idea, for many reasons - here are a few:
1. Although today's Google may handle the tilde, this doesn't mean that other programs will not have trouble. I'm not sure about the most recent versions, but Adobe's PDF Reader used to choke on urls that included tildes.
2. Log analysis software also comes to mind. It will probably be OK if character conversion is performed at the browser or server level first, as happens with "most" of these apps. Otherwise, who knows.
3. Webmasters actually typing your urls, rather than doing a copy/paste, may also not get it right. For one thing, not all keyboards even HAVE the stand-alone tilde character and these will require keystroke combinations. This could cost you backlinks.
4. The tilde is not widely known as a stand-alone character, but only as a diacritic mark placed ABOVE a basic character in some languages -- such as the widely recognized Spanish (ñ) character. If your link is lucky enough to get a press mention in a newspaper or magazine, a stand-alone tilde might well be typeset as a hyphen.
5. The tilde is among the ASCII characters whose positions are sometimes replaced by regional/national alphabet letters. For example, the code position that tilde is assigned in international ascii has u umlaut (ü) in several variants of ASCII, the German sharp "s" (ß) in German ASCII, etc. So beyond the keyboard problems I mentioned earlier, this oddity can sometimes cause incorrect representations on both screen and paper
Even the %7e substitution can be a problem. When a % is handwritten, it might later look like an ampersand (&) for instance.