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Using Raman spectroscopy to study the correlated 4d-electron metal Sr₂RhO₄, we observe pronounced excitations at 220 meV and 240 meV with A_1g and B_1g symmetries, respectively. We identify them as transitions between the spin-orbit multiplets of the Rh ions, in close analogy to the spin-orbit excitons in Mott insulators Sr₂IrO₄ and α-RuCl₃. This observation provides direct evidence for the unquenched spin-orbit coupling in Sr₂RhO₄. A quantitative analysis of the data reveals that the tetragonal crystal eld ∆ in Sr₂RhO₄ has a sign opposite to that in insulating Sr₂IrO₄, which enhances the planar xy orbital character of the effective J = 1/2 wavefunction. This supports a metallic ground state, and suggests that the c-axis compression of Sr₂RhO₄ may transform it into a quasi-two dimensional antiferromagnetic insulator.