Context: .Protoplanetary nebulae typically present non-spherical envelopes. The origin of such geometry is still controversial. There are indications that it may be carried over from an earlier phase of stellar evolution, such as the AGB phase. But how early in the star's evolution does the non-spherical envelope appear? Aims.Li-rich giants show dusty circumstellar envelopes that can help answer that question. We study a sample of fourteen Li-rich giants using optical polarimetry in order to detect non-spherical envelopes around them. Methods.We used the IAGPOL imaging polarimeter to obtain optical linear polarization measurements in {V} band. Foreground polarization was estimated using the field stars in each CCD frame.Results.After foreground polarization was removed, seven objects presented low intrinsic polarization (0.19-0.34)% and two (V859 Aql and GCSS 557) showed high intrinsic polarization values (0.87-1.16)%. This intrinsic polarization suggests that Li-rich giants present a non-spherical distribution of circumstellar dust. The intrinsic polarization level is probably related to the viewing angle of the envelope, with higher levels indicating objects viewed closer to edge-on. The correlation of the observed polarization with optical color excess gives additional support to the circumstellar origin of the intrinsic polarization in Li-rich giants. The intrinsic polarization correlates even better with the IRAS 25 μ m far infrared emission. Analysis of spectral energy distributions for the sample show dust temperatures for the envelopes that tend to be between 190 and 260 K. We suggest that dust scattering is indeed responsible for the optical intrinsic polarization in Li-rich giants.Conclusions.Our findings indicate that non-spherical envelopes may appear as early as the red giant phase of stellar evolution.