Consciousness is really just a name for having a model of yourself which you can reflect on and act on - plus a whole bunch of other confused interpretations which don't really add much.

To do anthropic reasoning you have to have a simple model of yourself which you can reason about.

Machines can do this too, of course, without too much difficulty. That typically makes them conscious, though. Perhaps we can imagine a machine performing anthropic reasoning while dreaming - i.e. when most of its actuators are disabled, and it would not normally be regarded as being conscious. However, then, how would we know about its conclusions?