We report a search for linear polarization in the active galactic nucleus (AGN) 3C 84 (NGC 1275) at observed frequencies of 239 and 348 GHz, corresponding to rest-frame frequencies of 243 and 354 GHz. We collected polarization data with the IRAM Plateau de Bure Interferometer via Earth rotation polarimetry. We do not detect linear polarization. Our analysis finds 3σ upper limits on the degree of polarization of 0.5 and 1.9 per cent at 239 and 348 GHz, respectively. We regard the influence of Faraday conversion as marginal, leading to expected circular polarizations ≲0.3 per cent. Assuming depolarization by a local Faraday screen, we constrain the rotation measure, as well as the fluctuations therein, to be ≳ 106 rad m−2. From this we estimate line-of-sight magnetic field strengths of ≳100 μG. Given the physical dimensions of 3C 84 and its observed structure, the Faraday screen appears to show prominent small-scale structure, with ΔRM ≳ 106 rad m−2 on projected spatial scales ≲1 pc.