ABSTRACT We present the weak-lensing mass calibration of the stellar-mass-based μ⋆ mass proxy for redMaPPer galaxy clusters in the Dark Energy Survey Year 1. For the first time, we are able to perform a calibration of μ⋆ at high redshifts, z > 0.33. In a blinded analysis, we use ∼6000 clusters split into 12 subsets spanning the ranges 0.1 ≤ z < 0.65 and μ⋆ up to ${∼} 5.5 \times 10^{13} \, \mathrm{M}_{⊙ }$, and infer the average masses of these subsets through modelling of their stacked weak-lensing signal. In our model, we account for the following sources of systematic uncertainty: shear measurement and photometric redshift errors, miscentring, cluster-member contamination of the source sample, deviations from the Navarro–Frenk–White halo profile, halo triaxiality, and projection effects. We use the inferred masses to estimate the joint mass–μ⋆–z scaling relation given by $〈 M_{200c} | μ _{⋆ },z 〉 = M_0 (μ _{⋆ }/5.16\times 10^{12} \, \mathrm{M_{\odot }})^{F_{μ _{⋆ }}} ((1+z)/1.35)^{G_z}$. We find $M_0= (1.14 ± 0.07) \times 10^{14} \, \mathrm{M_{\odot }}$ with $F_{μ _{⋆ }}= 0.76 ± 0.06$ and Gz = −1.14 ± 0.37. We discuss the use of μ⋆ as a complementary mass proxy to the well-studied richness λ for: (i) exploring the regimes of low z, λ < 20 and high λ, z ∼ 1; and (ii) testing systematics such as projection effects for applications in cluster cosmology.