  We take advantage of the wealth of rotation measures data contained in the
NRAO VLA Sky Survey catalogue to derive new, statistically robust, upper limits
on the strength of extragalactic magnetic fields. We simulate the extragalactic
magnetic field contribution to the rotation measures for a given field strength
and correlation length, by assuming that the electron density follows the
distribution of Lyman-$\alpha$ clouds. Based on the observation that rotation
measures from distant radio sources do not exhibit any trend with redshift,
while the extragalactic contribution instead grows with distance, we constrain
fields with Jeans' length coherence length to be below 1.7~nG at the $2\sigma$
level, and fields coherent across the entire observable Universe below 0.65~nG.
These limits do not depend on the particular origin of these cosmological
fields.
