We report on the synthesis and the superconductivity in Zr₄Rh₂O_x (x = 0.4, 0.5, 0.6, 0.7, 1.0). These compounds crystallize in the η-carbide structure, which is a filled version of the complex intermetallic Ti₂Ni structure. We find that in the system Zr₄Rh₂O_x, already a small amount (x ≥ 0.4) of oxygen addition stabilizes the η-carbide structure over the more common intermetallic CuAl₂ structure-type, in which Zr₂Rh crystallizes. We show that Zr₄Rh₂O_0.7 and Zr₄Rh₂O are bulk superconductors with critical temperatures of T_c ≈ 2.8 K and 4.7 K in the resistivity, respectively. Our analysis of the superconducting properties reveal both compounds to be strongly type-II superconductors with critical fields up to μ₀H_c1(0) ≈ 8.8 mT and μ₀H_c2(0) ≈ 6.08 T. Our results support that the η-carbides are a versatile family of compounds for the investigation of the interplay of interstitial doping on physical properties, especially for superconductivity.