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We present weak gravitational lensing measurements of a sample of 157clusters within the Kilo Degree Survey (KiDS), detected with a $>5\sigma$thermal Sunyaev-Zel'dovich (SZ) signal by the Atacama Cosmology Telescope(ACT). Using a halo-model approach we constrain the average total cluster mass,$M_{\rm WL}$, accounting for the ACT cluster selection function of the fullsample. We find that the SZ cluster mass estimate $M_{\rm SZ}$, which wascalibrated using X-ray observations, is biased with $M_{\rm SZ}/M_{\rm WL} =(1-b_{\rm SZ}) = 0.65\pm 0.05$. Separating the sample into six mass bins, wefind no evidence of a strong mass-dependency for the mass bias, $(1-b_{\rmSZ})$. Adopting this ACT-KiDS SZ mass-calibration would bring the Planck SZcluster count into agreement with the counts expected from the {\it Planck}cosmic microwave background $\Lambda$CDM cosmological model, although it shouldbe noted that the cluster sample considered in this work has a lower averagemass $M_{\rm SZ, uncor} = 3.64 \times 10^{14} M_{\odot}$ compared to the Planckcluster sample which has an average mass in the range $M_{\rm SZ, uncor} =(5.5-8.5) \times 10^{14} M_{\odot}$, depending on the sub-sample used.

ACT-DR5 Sunyaev-Zel'dovich Clusters: weak lensing mass calibration with KiDS