  We present an 8 sigma detection of cosmic magnification measured by the
variation of quasar density due to gravitational lensing by foreground large
scale structure. To make this measurement we used 3800 square degrees of
photometric observations from the Sloan Digital Sky Survey (SDSS) containing
\~200,000 quasars and 13 million galaxies. Our measurement of the galaxy-quasar
cross-correlation function exhibits the amplitude, angular dependence and
change in sign as a function of the slope of the observed quasar number counts
that is expected from magnification bias due to weak gravitational lensing. We
show that observational uncertainties (stellar contamination, Galactic dust
extinction, seeing variations and errors in the photometric redshifts) are well
controlled and do not significantly affect the lensing signal. By weighting the
quasars with the number count slope, we combine the cross-correlation of
quasars for our full magnitude range and detect the lensing signal at >4 sigma
in all five SDSS filters. Our measurements of cosmic magnification probe scales
ranging from 60 kpc/h to 10 Mpc/h and are in good agreement with theoretical
predictions based on the WMAP concordance cosmology. As with galaxy-galaxy
lensing, future measurements of cosmic magnification will provide useful
constraints on the galaxy-mass power spectrum.
