  We report Faraday rotation measurements of 11 extragalactic radio sources
with lines of sight through the Rosette Nebula, a prominent HII region
associated with the star cluster NGC 2244. It is also a prototypical example of
a "stellar bubble" produced by the winds of the stars in NGC 2244. The goal of
these measurements is to better determine the strength and structure of the
magnetic field in the nebula. We calculate the rotation measure (RM) through
two methods, a least-squares fit to $\chi$( $\lambda^2$) and Rotation Measure
Synthesis. In conjunction with our results from Savage et al. (2013), we find
an excess RM due to the shell of the nebula of +40 to +1200 rad m$^{-2}$ above
a background RM of +147 rad m$^{-2}$. We discuss two forms of a simple shell
model intended to reproduce the magnitude of the observed RM as a function of
distance from the center of the Rosette Nebula. The models represent different
physical situations for the magnetic field within the shell of the nebula. The
first assumes that there is an increase in the magnetic field strength and
plasma density at the outer radius of the HII region, such as would be produced
by a strong magnetohydrodynamic shock wave. The second model assumes that any
increase in the RM is due solely to an increase in the density, and the
Galactic magnetic field is unaffected in the shell. We employ a Bayesian
analysis to distinguish between the two forms of the model.
