  Intracluster magnetic fields with $ \sim \mu G $ strength induce Faraday
rotation on the cosmic microwave background
  (CMB) polarization. Measurements of this effect can potentially probe the
detailed structure of intracluster magnetic fields across clusters, since the
CMB polarization is a continuously varying field on the sky, in contrast to the
conventional method restricted by the limited number of radio sources behind or
inside a cluster. We here construct a method for extracting information on
magnetic fields from measurements of the effect, combined with possible
observations of the Sunyaev-Zel'dovich effect and X-ray emission for the same
cluster which are needed to reconstruct the electron density fields.
  Employing the high-resolution magneto-hydrodynamic simulations performed by
Dolag, Bartelmann & Lesch (1999) as a realistic model of magnetized
intracluster gas distribution, we demonstrate how our reconstruction technique
can well reproduce the magnetic fields, i.e., the spherically average radial
profiles of the field strength and the coherence length.
