  Using $N$-body simulations of cosmological large-scale structure formation,
for the first time, we show that the anisotropic primordial non-Gaussianity
(PNG) causes a scale-dependent modification, given by $1/k^2$ at small $k$
limit, in the three-dimensional power spectra of halo shapes (intrinsic
alignments), whilst the conventional power spectrum of halo number density
field remains unaffected. We discuss that wide-area imaging and spectrocopic
surveys observing the same region of the sky allow us to constrain the
quadrupole PNG coefficient $f_{\rm NL}^{s=2}$ at a precision comparable with or
better than that of the cosmic microwave background.
