I think it would be more correct to say that the act of measuring causes
the wave function collapse. I don't think the Copenhagen interpretation
itself says anything specific about consciousness. Neither is any attempt
made to define what exactly an act of measurement is.
Some other physicists (I think Eugene Wigner is one of the main ones) have
suggested the idea that consciousness is primary in inducing collapse.
A good experiment to keep in mind is the two slit interference experiment,
where measures are added to see which slot the particle goes through.
When this is done, coherence is lost and the interference pattern goes
away. This happens independent of whether or not anybody actually looks
at the measurements of which slit was used. This seems inconsistent with
the notion that consciousness collapses the wave function.
Hal