Swung dash or something like it. It shouldn't be raised like the tilde character U+02DC, and needs to be large enough to stand out in technical text, but may or may not be as wide as the swung dash ⁓.

The character is used in programming languages, in which usage it is best if it aligns vertically with =.

I can't think of a use for this character in which it would be desirable for the glyph to be raised to the height of a diacritic mark.

From the MS character design standards:

* ASCII tilde
Unicode: U+007E

Design : This character is used in mathematics as an operator for 'is proportional or similar to'. This character is also commonly used in text as a sign of approximation. The double tilde U+2248 is the correct mathematical operator for ' is approximately equal to'.

Example of common usage : One inch is ~72 point in traditonal typography.

This is not the same design and character as the lowercase spacing tilde diacritic.

Alignment : Vertically centers on the plus sign.

Advance width : Advance width should be the same as the figure space width.

Spacing : This character should space between figure zeros.

I've managed to get this character to fit nicely on the end of lower-case italic letters, as a kind of swash.
Also, in some fonts I've kerned it to make a wavy rule when repeated.

It's also used as a kind of emdash in early, two-CD releases in Japan. For example, the two-CD set of Bruce Springsteen's The River has a separate catalog number for each disc -- 50DP 355 and 50DP 356 -- and on the package spine the catalog number is shown as "50DP 355~6".

Another fairly common use in dictionaries: