Due to the generally delocalized nature of molecular valence orbitals, valence-shell spectroscopies do not usually allow to specifically target a selected atom in a molecule. However, in X-ray electron spectroscopy, the photoelectron momentum is large and the recoil angular momentum transferred to the molecule is larger when the photoelectron is ejected from a light atom compared with a heavy one. This confers an extreme sensitivity of the rotational excitation to the ionization site. Here we show that, indeed, the use of high-energy photons to photoionize valence-shell electrons of hydrogen chloride offers an unexpected way to decrypt the atomic composition of the molecular orbitals due to the rotational dependence of the photoionization profiles. The analysis of the site-specific rotational envelopes allows us to disentangle the effects of the two main mechanisms of rotational excitation, based on angular momentum exchange between the molecule and either the incoming photon or the emitted electron.