Alignments in the angular momentum vectors of galaxies can induce large scale correlations in their projected orientations. Such alignments arise from the tidal torques exerted on neighboring proto-galaxies by the smoothly varying shear field. Weak gravitational lensing can also induce ellipticity correlations since the images of neighboring galaxies will be distorted coherently by the intervening mass distribution. Comparing these two sources of shape correlations, it is found that for current weak lensing surveys with a median redshift of z_m=1, the intrinsic signal is a contaminant on the order of 1-10% of the measured signal. However, for shallower surveys with , the intrinsic correlations dominate over the lensing signal. The distortions induced by lensing are curl-free, whereas those resulting from intrinsic alignments are not. This difference can be used to disentangle these two sources of ellipticity correlations. When the distortions are dominated by lensing, as occurs at high redshifts, the decomposition provides a valuable tool for understanding properties of the noise and systematic errors.