  The electric field gradient (EFG) tensor at the $^{75}$As site couples to the
orbital occupations of the As p-orbitals and is a sensitive probe of local
nematicity in BaFe$_2$As$_2$. We use nuclear magnetic resonance to measure the
nuclear quadrupolar splittings and find that the EFG asymmetry responds
linearly to the presence of a strain field in the paramagnetic phase. We
extract the nematic susceptibility from the slope of this linear response as a
function of temperature and find that it diverges near the structural
transition in agreement with other measures of the bulk nematic susceptibility.
Our work establishes an alternative method to extract the nematic
susceptibility which, in contrast to transport methods, can be extended inside
the superconducting state.
