Cosmological simulations predict that an intergalactic magnetic field (IGMF) pervades the large scale structure (LSS) of the Universe. Measuring the IGMF is important to determine its origin (i.e. primordial or otherwise). Using data from the LOFAR Two Metre Sky Survey (LoTSS), we present the Faraday rotation measure (RM) and depolarisation properties of the giant radio galaxy J1235+5317, at a redshift of $z = 0.34$ and 3.38 Mpc in size. We find a mean RM difference between the lobes of $2.5pm0.1$ rad/m$^2$ , in addition to small scale RM variations of ~0.1 rad/m$^2$ . From a catalogue of LSS filaments based on optical spectroscopic observations in the local universe, we find an excess of filaments intersecting the line of sight to only one of the lobes. Associating the entire RM difference to these LSS filaments leads to a gas density-weighted IGMF strength of ~0.3 {mu}G. However, direct comparison with cosmological simulations of the RM contribution from LSS filaments gives a low probability (~5%) for an RM contribution as large as 2.5 rad/m$^2$ , for the case of IGMF strengths of 10 to 50 nG. It is likely that variations in the RM from the Milky Way (on 11 scales) contribute significantly to the mean RM difference, and a denser RM grid is required to better constrain this contribution. In general, this work demonstrates the potential of the LOFAR telescope to probe the weak signature of the IGMF. Future studies, with thousands of sources with high accuracy RMs from LoTSS, will enable more stringent constraints on the nature of the IGMF.
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