  We present experimental evidence for spin-orbit interaction of an electron as
it scatters from a neutral atom. The scattering process takes place within a
Rb$_2$ ultralong-range Rydberg molecule, consisting of a Rydberg atomic core, a
Rydberg electron, and a ground state atom. The spin-orbit interaction leads to
characteristic level splittings of vibrational molecular lines which we
directly observe via photoassociation spectroscopy. We benefit from the fact
that molecular states dominated by resonant $p$-wave interaction are
particularly sensitive to the spin-orbit interaction. Our work paves the way
for studying novel spin dynamics in ultralong-range Rydberg molecules.
Furthermore, it shows that the molecular setup can serve as a microlaboratory
to perform precise scattering experiments in the low-energy regime of a few
meV.
