We determined Faraday rotation measures (RMs) towards 137 pulsars in the northern sky, using Low-Frequency Array (LOFAR) observations at 110-190MHz. 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 0.1rad/m^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 0.001rad/m^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(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.