  We develop a novel method of measuring the lensing distortion profiles of
clusters with stacking the scaled amplitudes of background galaxy ellipticities
as a function of the scaled centric radius according to the NFW prediction of
each cluster, based on the assumption that the different clusters in a sample
follow the universal NFW profile. First we demonstrate the feasibility of this
method using both the analytical NFW model and simulated halos in
high-resolution $N$-body simulations. We then apply, as a proof of concept,
this method to the Subaru weak lensing data and the XMM/Chandra X-ray
observables for a sample of 50 massive clusters in the redshift range $0.15\le
z\le 0.3$, where their halo masses range over an order of magnitude. To
estimate the NFW parameters of each cluster, we use the halo mass proxy
relation of X-ray observables, based on either the hydrostatic equilibrium or
the gas mass, and then infer the halo concentration from the model $c(M)$
relation. We evaluate a performance of the NFW scaling analysis by measuring
the scatters of 50 cluster lensing profiles relative to the NFW predictions
over a range of radii, $0.14\le R/[h^{-1}{\rm Mpc}]\le 2.8$. We found a 4 -
6$\sigma$ level evidence of the universal NFW profile in 50 clusters, for both
the X-ray halo mass proxy relations, although the gas mass appears to be a
better proxy of the underlying true mass. By comparing the measurements with
the simulations of cluster lensing taking into account the statistical errors
of intrinsic galaxy shapes in the Subaru data, we argue that additional halo
mass errors or intrinsic scatters of $\sigma_{\ln M_{500c}}\sim 0.2$ - $0.3$
could reconcile a difference between the measurements and the simulations.
