  We investigate the orientation correlation of giant elliptical galaxies by
measuring the intrinsic ellipticity correlation function of 83,773 luminous red
galaxies (LRGs) at redshifts 0.16 -- 0.47 from the Sloan Digital Sky Survey. We
have accurately determined the correlation up to 30 $h^{-1}$Mpc. Luminosity
dependence of the ellipticity correlation is also detected although the error
bars are large, while no evidence is found for its redshift evolution between
$z=0.2$ and $z=0.4$. Then we use a cosmological $N$-body simulation to examine
misalignment between the central LRGs and their parent dark matter halos.
Central and satellite galaxies are assigned to simulated halos by employing a
halo occupation distribution model for the LRGs. The ellipticity correlation is
predicted to have the same shape as but an amplitude about 4 times higher than
our observation if the central LRGs are perfectly aligned with their host
halos. This indicates that the central LRG galaxies are preferentially but not
perfectly aligned with their host halos. With the assumption that there is a
misalignment angle between a central LRG and its host halo which follows a
Gaussian distribution with a zero mean and a width $\sigma_\theta$, we obtain a
tight constraint on the misalignment parameter,
$\sigma_\theta={35.4}^{+4.0}_{-3.3}$ deg. This type of intrinsic ellipticity
correlation, if not corrected, can lead to contamination at 5% level to the
shear power spectrum in weak lensing surveys of limiting magnitude
$R_{AB}=24.5$ if the source central galaxies follow the same misalignment
distribution as the LRGs.
