  We estimate the effects of weak lensing by large-scale density
inhomogeneities and long-wavelength gravitational waves upon the polarization
properties of electromagnetic radiation as it propagates from cosmologically
distant sources. Scalar (density) fluctuations do not rotate neither the plane
of polarization of the electromagnetic radiation nor the source image. They
produce, however, an appreciable shear, which distorts the image shape, leading
to an apparent rotation of the image orientation relative to its plane of
polarization. In sources with large ellipticity the apparent rotation is rather
small, of the order (in radians) of the dimensionless shear. The effect is
larger at smaller source eccentricity. A shear of 1% can induce apparent
rotations of around 5 degrees in radio sources with the smallest eccentricity
among those with a significant degree of integrated linear polarization. We
discuss the possibility that weak lensing by shear with rms value around or
below 5% may be the cause for the dispersion in the direction of integrated
linear polarization of cosmologically distant radio sources away from the
perpendicular to their major axis, as expected from models for their magnetic
fields. A rms shear larger than 5% would be incompatible with the observed
correlation between polarization properties and source orientation in distant
radio galaxies and quasars. Gravity waves do rotate both the plane of
polarization as well as the source image. Their weak lensing effects, however,
are negligible.
