Is it possible for a player to add upload/import photo/map?

I am wondering if I can give the end user the ability to upload or import there own texture maps?

Example: So the player could import a picture of their own face to be mapped onto a character model.

You mean like the example on this page:

Another similar feature on the roadmap for Unity 3.5 (but currently not available) is access to webcam. This will let you take a picture from a webcam and use it as a texture in a game.

See more here: