Herein, we utilize surface-enhanced hyper-Raman scattering (SEHRS) under resonance conditions to probe the adsorbate geometry of rhodamine 6G (R6G) on silver colloids. Our results show resonance SEHRS is highly sensitive to molecular orientation due to non-Condon effects, which do not appear in its linear counterpart surface-enhanced Raman scattering. Comparisons between simulated and measured SEHRS spectra reveal R6G adsorbs mostly perpendicular to the nanoparticle surface along the ethylamine groups with the xanthene ring oriented edgewise. Our results expand upon previous studies that rely on indirect, qualitative probes of R6G’s orientation on plasmonic substrates. More importantly, this work represents the first determination of adsorbate geometry by SEHRS and opens up the possibility to study the orientation of single molecules in complex, plasmonic environments.