I'm pretty sure it can't. There's nothing in a WAV file that's meant to be executed. A quick google turns up a DirectX vulnerability from 2007 (a validation error that's not inherent to the WAV format per se), and a recent case of WAV files being used to conceal malicious payloads (but coupled with a loader).
Having said that, the "arbitrary code" found in TrueType is not really arbitrary either - it's not supposed to be able to do anything except change the appearance of the font. From a security standpoint, there's no theoretical difference between a WAV and a TTF font - neither can hurt your machine if the loader is bug-free. Practically speaking though, a font renderer that needs to implement a sort of virtual machine is more complex, and therefore more likely to have exploitable bugs, than a WAV renderer that simply needs to swap a few bytes around and shove them at a DAC.
No, TTF is fully turning complete. Maybe I should have specified that in the original post. WAV is just "vibrate speaker this way" over and over again.
I realize this, but the fact that the format is "Turing complete" doesn't actually have any direct bearing on whether it's exploitable. Because the input to a TTF engine is not actually x86 machine code, it's misleading to frame it as "arbitrary code in ring0". It's not arbitrary - it can't do anything unless the TTF engine has bugs. And any format loader can have exploitable bugs, not just Turing complete ones.
Security wise, Turing completeness doesn't matter[note]. All that really matters is that the implementation of the format is complex. H264 is not Turing complete, but it is complex, and thus a frequent source of vulnerabilities. Conversely you could probably put a toy Brainfuck interpreter in ring0 and, with moderate care, be confident that no malicious Brainfuck code can take over your system.
[note] It matters a little bit if you consider it a "security" problem that you lose any guarantees of how long a file might take to load. A malicious file could infinite loop, and thus deny service. But then again, this isn't restricted to Turing complete formats - a zip bomb can also deny service this way.
