  We studied the polarization behavior of the quasar 3C 273 over the 1 mm
wavelength band at ALMA with a total bandwidth of 7.5GHz across 223 to 243 GHz
at 0.8 arcsec resolution, corresponding to 2.1 kpc at the distance of 3C 273.
With these observations we were able to probe the optically thin polarized
emission close to the jet base, and constrain the magnetic field structure. We
computed the Faraday rotation measure using simple linear fitting and Faraday
rotation measure synthesis. In addition, we modeled the broadband behavior of
the fractional Stokes Q and U parameters (qu-fitting). The systematic
uncertainties in the polarization observations at ALMA were assessed through
Monte Carlo simulations. We find the unresolved core of 3C 273 to be 1.8%
linearly polarized. We detect a very high rotation measure (RM) of ~5.0 x10^5
rad/m^2 over the 1 mm band when assuming a single polarized component and an
external RM screen. This results in a rotation of >40 deg of the intrinsic
electric vector position angle, which is significantly higher than typically
assumed for millimeter wavelengths. The polarization fraction increases as a
function of wavelength, which according to our qu-fitting could be due to
multiple polarized components of different Faraday depth within our beam, or
internal Faraday rotation. With our limited wavelength coverage, we cannot
distinguish between the cases, and additional multifrequency and high angular
resolution observations are needed to determine the location and structure of
the magnetic field of the Faraday active region. Comparing our RM estimate with
values obtained at lower frequencies, the RM increases as a function of
observing frequency, following a power law with an index of ~2.0 consistent
with a sheath surrounding a conically expanding jet. We also detect ~0.2%
circular polarization, although further observations are needed to confirm this
result.
