We report a detection of weak, tangential distortion of the images of
cosmologically distant, faint galaxies due to gravitational lensing by
foreground galaxies. A mean image polarization of (p) = 0.011 +/- 0.0
06 (95% confidence bounds) is obtained for 3202 pairs of source (23 <
r(s) less than or equal to 24) and lens (20 (20 less than or equal to
r(d) less than or equal to 23) galaxies with projected separations of
5 '' less than or equal to theta 34 ''. Averaged over annuli of inner
radius 5 '' and outer radius theta(max), the signal is string for lens
-source separations of theta(max) less than or similar to 90 '' consis
tent with quasi-isothermal galaxy halos extending to large radii (grea
ter than or similar to 100 h(-1) kpc). The observed polarization is al
so consistent with the signal expected on the basis of simulations inc
orporating measured properties of local galaxies and modest extrapolat
ions of the observed redshift distribution of faint galaxies (to which
the results are somewhat sensitive). From the simulations we obtain f
ormal best-fit model parameters for the dark halos of the lens galaxie
s that consist of a characteristic circular velocity of V similar to
220 +/- 80 km s(-1) and characteristic radial extent of s greater tha
n or similar to 100 h(-1) kpc. The predicted polarization based on the
model is relatively insensitive to the characteristic radial extent o
f the halos, s, and very small halos (s* similar to 10 h(-1) kpc) are
excluded only at the 2 sigma level. The formal best-fit halo paramete
rs imply typical masses for the lens galaxies within a radius of 100 h
(-1) kpc on the order of 1.0(-0.5)(+1.2) x 10(12) h(-1) M. (90% confid
ence bounds), in agreement with recent dynamical estimates of the mass
es of local spiral galaxies. This is particularly encouraging as the l
ensing and dynamical mass estimators rely on different sets of assumpt
ions. Contamination of the gravitational lensing signal by a populatio
n of tidally distorted satellite galaxies can be ruled out with reason
able confidence. The prospects for corroborating and improving this me
asurement seem good, especially using deep HST archival data.