  We present the first measurement of weak lensing by large-scale structure on
1-4 degree scales based on the FIRST Radio Survey, a quarter-sky, 20-cm survey
produced with the NRAO Very Large Array (VLA). The large angular scales provide
an unique measurement in the linear regime of the matter power spectrum. We use
the shapelet method to estimate the shear of radio sources derived directly
from the Fourier(uv) plane. With realistic simulations we verify that the
method yields unbiased shear estimators. We quantify and correct for the
systematic effects which can produce spurious shears, analytically and with
simulations. We measure the shear correlation functions on angular scales of
0.5-40 degrees, and compute the corresponding aperture mass statistics. On 1-4
degrees scales, we find that the B-modes are consistent with zero, and detect a
lensing E-mode signal significant at the 3.0 sigma level. After removing radio
sources with an optical counterpart, the E-mode signal increases by 10-20%, as
expected for a lensing signal derived from more distant sources. We use the
E-mode measurement to constrain the mass power spectrum normalization sigma_8
and the median redshift z_m of the unidentified radio sources. We find
sigma_8*(z_m/2)^(0.6) ~ 1.0 +/- 0.2, where the 1 sigma error bars include
statistical errors, cosmic variance, and systematics. This is consistent with
earlier determinations of sigma_8, and with our current knowledge of the
redshift distribution of radio sources. Taking the prior sigma_8 = 0.9 +/- 0.1
(68%CL) from the WMAP experiment, this corresponds to z_m = 2.2 +/- 0.9 (68%CL)
for radio sources without optical counterparts. Our results offer promising
prospects for precision measurements of cosmic shear with future radio
interferometers such as LOFAR and the SKA.
