In this paper we report on an investigation of statistical weak gravitational lensing of cosmologically distant faint galaxies by foreground galaxies. The signal we seek is a distortion of the images of faint galaxies resulting in a weakly preferred tangential alignment of faint galaxies around brighter galaxies. That is, if the faint galaxies have been gravitationally lensed by the brighter systems, the major axes of their images will tend to lie perpendicular to the radius vectors joining the centroids of the faint and bright galaxies (Fig. 1). Modeling a lens galaxy as a singular isothermal sphere with circular velocity Vc, an ellipticity of ∼ 2πVc2 /c2θ is induced in the image of a source galaxy at an angular separation θ from the lens. This is of order a few percent for faint–bright galaxy pairs with separations θ ∼ 30″ where the lens is a typical bright spiral. Over 1000 pairs must be measured in order to detect such a signal in the presence of the noise associated with the intrinsic galaxy shapes. Given a sufficiently large number of pairs, it may be possible to use the variation of the induced ellipticity with θ to study the angular extent of the halos of the lens galaxies.