  We present new measurements of cosmic microwave background (CMB) lensing over
$9400$ sq. deg. of the sky. These lensing measurements are derived from the
Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB dataset, which
consists of five seasons of ACT CMB temperature and polarization observations.
We determine the amplitude of the CMB lensing power spectrum at $2.3\%$
precision ($43\sigma$ significance) using a novel pipeline that minimizes
sensitivity to foregrounds and to noise properties. To ensure our results are
robust, we analyze an extensive set of null tests, consistency tests, and
systematic error estimates and employ a blinded analysis framework. The
baseline spectrum is well fit by a lensing amplitude of
$A_{\mathrm{lens}}=1.013\pm0.023$ relative to the Planck 2018 CMB power spectra
best-fit $\Lambda$CDM model and $A_{\mathrm{lens}}=1.005\pm0.023$ relative to
the $\text{ACT DR4} + \text{WMAP}$ best-fit model. From our lensing power
spectrum measurement, we derive constraints on the parameter combination
$S^{\mathrm{CMBL}}_8 \equiv \sigma_8 \left({\Omega_m}/{0.3}\right)^{0.25}$ of
$S^{\mathrm{CMBL}}_8= 0.818\pm0.022$ from ACT DR6 CMB lensing alone and
$S^{\mathrm{CMBL}}_8= 0.813\pm0.018$ when combining ACT DR6 and Planck NPIPE
CMB lensing power spectra. These results are in excellent agreement with
$\Lambda$CDM model constraints from Planck or $\text{ACT DR4} + \text{WMAP}$
CMB power spectrum measurements. Our lensing measurements from redshifts
$z\sim0.5$--$5$ are thus fully consistent with $\Lambda$CDM structure growth
predictions based on CMB anisotropies probing primarily $z\sim1100$. We find no
evidence for a suppression of the amplitude of cosmic structure at low
redshifts
