  We use the measured scattering timescales of Fast Radio Bursts (FRBs) from
the CHIME catalog to derive an upper limit on the magnetic field on sub-kpc
scales in the intergalactic medium (IGM). A nonmagnetized, photoionized IGM is
insufficient to explain the turbulent scattering at all redshifts, with a
Warm-Hot component being marginally consistent with the data at $z \sim 1$.
Accounting for the lower envelope of the temporal smearing distribution with a
nonzero magnetic field leads to upper limits $B < 10-30$ nG on scales of
0.07-0.20 kpc in the IGM at $z \sim 1-2$. Our work introduces a novel technique
to constrain small-scale magnetic fields in the IGM, in a regime unexplored by
the Rotation and Dispersion Measures of FRBs.
