  We investigate the magnetic field power spectrum in the cool core galaxy
cluster A2199 by analyzing the polarized emission of the central radio source
3C338. The polarized radiation from the radio emitting plasma is modified by
the Faraday rotation as it passes through the magneto-ionic intracluster
medium. We use Very Large Array observations between 1665 and 8415 MHz to
produce detailed Faraday rotation measure and fractional polarization images of
the radio galaxy. We simulate Gaussian random three-dimensional magnetic field
models with different power-law power spectra and we assume that the field
strength decreases radially with the thermal gas density as n_e^{\eta}. By
comparing the synthetic and the observed images with a Bayesian approach, we
constrain the strength and structure of the magnetic field associated with the
intracluster medium. We find that the Faraday rotation toward 3C338 in A2199 is
consistent with a magnetic field power law power spectrum characterized by an
index n=(2.8 \pm 1.3) between a maximum and a minimum scale of fluctuation of
\Lambda_{max}=(35 \pm 28) kpc and \Lambda_{min}=(0.7 \pm 0.1) kpc,
respectively. By including in the modeling X-ray cavities coincident with the
radio galaxy lobes, we find a magnetic field strength of <B_0>=(11.7 \pm 9.0)
\mu G at the cluster center. Further out, the field decreases with the radius
following the gas density to the power of \eta=(0.9 \pm 0.5).
