We have studied the linear polarization of 86 active galactic nuclei (AGN) in the observed frequency range 80-267 GHz (3.7-1.1mm in wavelength), corresponding to rest-frame frequencies 82-738 GHz, with the IRAM Plateau de Bure Interferometer (PdBI). The large number of measurements, 441, makes our analysis the largest polarimetric AGN survey in this frequency range to date. We extracted polarization parameters via earth rotation polarimetry with unprecedented median precisions of ~0.1% in polarization fractions and ~1.2 degrees in polarization angles. For 73 of 86 sources we detect polarization at least once. The degrees of polarization are as high as ~19%, with the median over all sources being ~4%. Source fluxes and polarizations are typically highly variable, with fractional variabilities up to ~60%. We find that BLLac sources have on average the highest level of polarization. There appears to be no correlation between degree of polarization and redshift, indicating that there has been no substantial change of polarization properties since z~2.4. Our polarization and spectral index distributions are in good agreement with results found from various samples observed at cm/radio wavelengths; thus our frequency range is likely tracing the signature of synchrotron radiation without noticeable contributions from other emission mechanisms. The millimeter-break located at frequencies >1 THz appears to be not detectable in the frequency range covered by our survey.