  We determined Faraday rotation measures (RMs) towards 137 pulsars in the
northern sky, using Low-Frequency Array (LOFAR) observations at 110-190 MHz.
This low-frequency RM catalogue, the largest to date, improves the precision of
existing RM measurements on average by a factor of 20 - due to the low
frequency and wide bandwidth of the data, aided by the RM synthesis method. We
report RMs towards 25 pulsars for the first time. The RMs were corrected for
ionospheric Faraday rotation to increase the accuracy of our catalogue to
approximately 0.1 rad m$^{\rm -2}$. The ionospheric RM correction is currently
the largest contributor to the measurement uncertainty. In addition, we find
that the Faraday dispersion functions towards pulsars are extremely Faraday
thin - mostly less than 0.001 rad m$^{\rm -2}$. We use these new precise RM
measurements (in combination with existing RMs, dispersion measures, and
distance estimates) to estimate the scale height of the Galactic halo magnetic
field: 2.0$\pm$0.3 kpc for Galactic quadrants I and II above and below the
Galactic plane (we also evaluate the scale height for these regions
individually). Overall, our initial low-frequency catalogue provides valuable
information about the 3-D structure of the Galactic magnetic field.
