  We show with analytic models that the assumption of uncorrelated intrinsic
ellipticities of target sources that is usually made in searches for weak
gravitational lensing due to large-scale mass inhomogeneities (``field
lensing'') is unwarranted. If the orientation of the galaxy image is determined
either by the angular momentum or the shape of the halo in which it forms, then
the image should be aligned preferentially with the component of the tidal
gravitational field perpendicular to the line of sight. Long-range correlations
in the tidal field will thus lead to long-range ellipticity-ellipticity
correlations that mimic the shear correlations due to weak gravitational
lensing. We calculate the ellipticity-ellipticity correlation expected if halo
shapes determine the observed galaxy shape, and we discuss uncertainties (which
are still considerable) in the predicted amplitude of this correlation. The
ellipticity-ellipticity correlation induced by angular momenta should be
smaller. We consider several methods for discriminating between the
weak-lensing (extrinsic) and intrinsic correlations, including the use of
redshift information. An ellipticity--tidal-field correlation also implies the
existence of an alignment of images of galaxies near clusters. Although the
intrinsic alignment may complicate the interpretation of field-lensing results,
it is inherently interesting as it may shed light on galaxy formation as well
as on structure formation.
