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We present a measurement of the cross-correlation between theMagLimgalaxies selected from the Dark Energy Survey (DES) first three years of observations (Y3) and cosmic microwave background (CMB) lensing from the Atacama Cosmology Telescope (ACT) Data Release 4 (DR4), reconstructed over ∼ 436 sq. deg of the sky. Our galaxy sample, which covers ∼ 4143 sq. deg, is divided into six redshift bins spanning the redshift range of 0.20 < z < 1.05. We adopt a blinding procedure until passing all consistency and systematics tests. After imposing scale cuts for the cross-power spectrum measurement, we reject the null hypothesis of no correlation at 9.1σ. We constrain cosmological parameters from a joint analysis of galaxy and CMB lensing-galaxy power spectra considering a flat ΛCDM model, marginalized over 23 astrophysical and systematic nuisance parameters. We find the clustering amplitude S_8 ≡ σ_8(Ω_m/0.3)^0.5 = 0.75+0.04-0.05. In addition, we constrain the linear growth of cosmic structure as a function of redshift. Our results are consistent with recent DES Y3 analyses and suggest a preference for a lower S_8 compared to results from measurements of CMB anisotropies by the Planck satellite, although at a mild level (< 2σ) of statistical significance.