Guides:Avatar Change Voice Position
[Reason: You can contribute by expanding and proofreading this article, in accordance with the Manual of Style.]
VRChat currently does not have a supported way to change where your voice on your avatar comes from. This is a unintended feature, and may break in the future. This trick also does not support generic avatars.
Normally VRChat has the players voice follow the avatars humanoid configured head bone. So with constraints you can move your head bone, and your voice will move along with it. If you don't want your avatars head detached or stretched it will require a little more setup.
Setup

First you will need to modify your avatar (This is usually done in something like blender) to have two head bones. First one is will have no weight painting, this will be your humanoid configured head. The second will have the head mesh weight painted to it, and any extra bones for example ears will be on this one. This second head bone will be the visual head that people see.
Next is to setup the head bones in Unity. First go to the rig humanoid configuration menu. Here you will need to make sure your avatars humanoid head bone with no weight painting is configured as the head.