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It is well established that a rotational symmetry breaking electronic nematic phase is ubiquitous in the phase diagrams of iron-based superconductors and that anisotropic strain is a uniquely powerful in-situ probe of electronic anisotropy in these systems. In this work we present a new transport coefficient, the elasto-Hall coefficient, which is the response of the Hall coefficient to externally applied strain. We show that in the Co-doped BaFe₂As₂ system, this effect is dominated by a nonlinear response in the B_2g symmetry channel which is large and strongly temperature dependent. In the optimally doped composition near the nematic quantum critical point, this nonlinear coefficient diverges towards zero temperature. Combining this elasto-Hall measurement with elastoresistivity, we argue that our observations are consistent with enhanced interband scattering from spin fluctuations as a result of B_2g strain.