摘要： Context. Measuring and calibrating relations between cluster observables is critical for resource-limited studies. The mass–richness relation of clusters offers an observationally inexpensive way of estimating masses. Its calibration is essential for cluster and cosmological studies, especially for high-redshift clusters. Weak gravitational lensing magnification is a promising and complementary method to shear studies, that can be applied at higher redshifts. Aims. We aim to employ the weak lensing magnification method to calibrate the mass–richness relation up to a redshift of 1.4. We used the Spitzer Adaptation of the Red-Sequence Cluster Survey (SpARCS) galaxy cluster candidates (0.2 < z < 1.4) and optical data from the Canada France Hawaii Telescope (CFHT) to test whether magnification can be effectively used to constrain the mass of high-redshift clusters. Methods. Lyman-break galaxies (LBGs) selected using the u-band dropout technique and their colours were used as a background sample of sources. LBG positions were cross-correlated with the centres of the sample of SpARCS clusters to estimate the magnification signal, which was optimally-weighted using an externally-calibrated LBG luminosity function. The signal was measured for cluster sub-samples, binned in both redshift and richness. Results. We measured the cross-correlation between the positions of galaxy cluster candidates and LBGs and detected a weak lensing magnification signal for all bins at a detection significance of 2.6–5.5σ. In particular, the significance of the measurement for clusters with z > 1.0 is 4.1σ; for the entire cluster sample we obtained an average M200 of 1.28 +0.23 ?0.21 × 1014 M⊙. Conclusions. Our measurements demonstrated the feasibility of using weak lensing magnification as a viable tool for determining the average halo masses for samples of high redshift galaxy clusters. The results also established the success of using galaxy over-densities to select massive clusters at z > 1. Additional studies are necessary for further modelling of the various systematic effects we discussed.