Context : Aims : We studied the polarization behavior of the quasar 3C 273 over the 1 mm wavelength band at ALMA with a total bandwidth of 7.5 GHz across 223 to 243 GHz at 0.8″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 . Methods : 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 . Results : 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 \pm 0.3 ) \times 10 ^ { 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 \degr 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 can not 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 \pm 0.2 , consistent with a sheath surrounding a conically expanding jet . We also detect \sim 0.2 % circular polarization , although further observations are needed to confirm this result . Conclusions :