They don't really know, but the evidence suggests that it doesn't, or at least hasn't yet. There have been a few studies following up on groups of people who consumed CWD positive deer.

https://www.usatoday.com/story/news/health/2019/02/21/zombie...

No. But Mad Cow Disease (also caused by prions) sure did. More info: https://en.wikipedia.org/wiki/Bovine_spongiform_encephalopat...