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 223–243 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 ± 0.3) × 105 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° 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 to 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 ± 0.2, 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.