  We extend the description of the isotropic and anisotropic random component
of the small-scale magnetic field within the existing magnetic field model of
the Milky Way from Jansson&Farrar, by including random realizations of the
small-scale component. Using a magnetic-field power spectrum with Gaussian
random fields, the NE2001 model for the thermal electrons and the Galactic
cosmic-ray electron distribution from the current GALPROP model we derive
full-sky maps for the total and polarized synchrotron intensity as well as the
Faraday rotation-measure distribution. While previous work assumed that
small-scale fluctuations average out along the line-of-sight or which only
computed ensemble averages of random fields, we show that these fluctuations
need to be carefully taken into account. Comparing with observational data we
obtain not only good agreement with 408 MHz total and WMAP7 22 GHz polarized
intensity emission maps, but also an improved agreement with Galactic
foreground rotation-measure maps and power spectra, whose amplitude and shape
strongly depend on the parameters of the random field. We demonstrate that a
correlation length of ~220pc (50pc being a 5\sigma lower limit) is needed to
match the slope of the observed power spectrum of Galactic foreground
rotation-measure maps. Using multiple realizations allows us also to infer
errors on individual observables. We find that previously-used amplitudes for
random and anisotropic random magnetic field components need to be rescaled by
factors of ~0.3 and 0.6 to account for the new small-scale contributions. Our
model predicts a rotation measure of -2.8\pm7.1 rad/m^2 and 4.4\pm11.0 rad/m^2
for the north and south Galactic poles respectively, in good agreement with
observations. Applying our model to deflections of ultra-high-energy cosmic
rays we infer a mean deflection of ~3.5\pm1.1 degree for 60 EeV protons
arriving from CenA.
