We present subarcsecond resolution polarimetric observations of the 878 \mu m thermal dust continuum emission obtained with the Submillimeter Array ( SMA ) towards the IRAS 16293 - 2422 protostellar binary system . We report the detection of linearly polarized dust emission arising from the circumstellar disk associated with the IRAS 16293 - 2422 B protostar . The fractional polarization of \simeq 1.4 % is only slightly lower than that expected from theoretical calculations in such disks . The magnetic field structure on the plane of the sky derived from the dust polarization suggests a complex magnetic field geometry in the disk , possibly associated with a rotating disk that is wrapping the field lines as expected from the simulations . The polarization around IRAS 16293 - 2422 A at sub-arcsecond angular resolution is only marginally detected .