  We use polarised neutron diffraction to study the induced magnetization
density of near optimally doped Ba(Fe0.935Co0.065)2As2 (T_C=24 K) as a function
of magnetic field (1<H<9 T) and temperature (2<T<300 K). The T-dependence of
the induced moment in the superconducting state is consistent with the Yosida
function, characteristic of spin-singlet pairing. The induced moment is
proportional to applied field for H < 9 T ~ Hc2/6. In addition to the Yosida
spin-susceptibility, our results reveal a large zero-field contribution M
(H=>0,T=>0)/H ~ 2/3 \chi_{normal} which does not scale with the field or number
of vortices and is most likely due to the van Vleck susceptibility. Magnetic
structure factors derived from the polarization dependence of 15 Bragg
reflections were used to make a maximum entropy reconstruction of the induced
magnetization distribution in real space. The magnetization is confined to the
Fe atoms and the measured density distribution is in good agreement with LAPW
band structure calculations which suggest that the relevant bands near the
Fermi energy are of the d_{xz/yz} and d_{xy} type.
