  The VST Optical Imaging of the CDFS and ES1 Fields (VOICE) Survey is a
Guaranteed Time program carried out with the ESO/VST telescope to provide deep
optical imaging over two 4 deg$^2$ patches of the sky centred on the CDFS and
ES1 pointings. We present the cosmic shear measurement over the 4 deg$^2$
covering the CDFS region in the $r$-band using LensFit. Each of the four tiles
of 1 deg$^2$ has more than one hundred exposures, of which more than 50
exposures passed a series of image quality selection criteria for weak lensing
study. The $5\sigma$ limiting magnitude in $r$- band is 26.1 for point sources,
which is $\sim$1 mag deeper than other weak lensing survey in the literature
(e.g. the Kilo Degree Survey, KiDS, at VST). The photometric redshifts are
estimated using the VOICE $u,g,r,i$ together with near-infrared VIDEO data
$Y,J,H,K_s$. The mean redshift of the shear catalogue is 0.87, considering the
shear weight. The effective galaxy number density is 16.35 gal/arcmin$^2$,
which is nearly twice the one of KiDS. The performance of LensFit on such a
deep dataset was calibrated using VOICE-like mock image simulations.
Furthermore, we have analyzed the reliability of the shear catalogue by
calculating the star-galaxy cross-correlations, the tomographic shear
correlations of two redshift bins and the contaminations of the blended
galaxies. As a further sanity check, we have constrained cosmological
parameters by exploring the parameter space with Population Monte Carlo
sampling. For a flat $\Lambda$CDM model we have obtained $\Sigma_8$ =
$\sigma_8(\Omega_m/0.3)^{0.5}$ = $0.68^{+0.11}_{-0.15}$.

Cosmology and Nongalactic Astrophysics