We present late-time radio observations of GW170817, the first binary neutron-star (NS) merger discovered through gravitational waves (GWs) by the advanced Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo detectors. Our observations, carried out with the Karl G. Jansky Very Large Array (VLA), were optimized to detect polarized radio emission, and thus to constrain the linear polarization fraction of GW170817. At an epoch of ≈244 days after the merger, we rule out linearly polarized emission above a fraction of ≈12% at a frequency of 2.8 GHz (99% confidence). Within the structured jet scenario (a.k.a. successful jet plus cocoon system) for GW170817, the derived upper limit on the radio continuum linear polarization fraction strongly constrains the magnetic field configuration in the shocked ejecta. We show that our results for GW170817 are compatible with the low level of linear polarization found in afterglows of cosmological long γ-ray bursts (GRBs). Finally, we discuss our findings in the context of future expectations for the study of radio counterparts of binary NS mergers identified by ground-based GW detectors.