The elastoresistivity tensor mij,kl relates changes in resistivity to strains experienced by a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, for a tetragonal material, the B1g and B2g components of the elastoresistivity tensor (mxx,xx - mxx,yy and 2mxy,xy, respectively) can be related to its nematic susceptibility. Previous experimental probes of this quantity have focused exclusively on differential longitudinal elastoresistance measurements, which determine the induced resistivity anisotropy arising from anisotropic in-plane strain based on the difference of two longitudinal resistivity measurements. Here we describe a complementary technique based on transverse elastoresistance measurements. This new approach is advantageous because it directly determines the strain-induced resistivity anisotropy from a single transverse measurement. To demonstrate the efficacy of this new experimental protocol, we present transverse elastoresistance measurements of the 2mxy,xy elastoresistivity coefficient of BaFe2As2, a representative iron-pnictide that has previously been characterized via differential longitudinal elastoresistance measurements.