The clearance that exists between the casing and turbine blade tips is one of the key drivers of efficiency in gas turbine engines. For this reason, engine manufacturers utilize precise manufacturing techniques and may use clearance control systems to minimize tip clearances to reduce associated losses. Despite these efforts, turbines typically exhibit some nominal casing ovality or rotor-casing eccentricity, and changes to blade tip clearance during operation commonly occur due to thermal and mechanical stresses. The present study investigates non-axisymmetric tip clearance effects by creating a rotor-casing eccentricity in a one-stage axial test turbine operating in a continuous-duration mode at engine-relevant conditions with engine representative hardware. A magnetic levitation bearing system was leveraged to move the turbine shaft to vary the rotor-casing eccentricity without test section disassembly. The results of this study indicate that rotor-casing eccentricity does not affect overall turbine efficiency over the range that was tested, but does locally influence efficiency and the rotor exit flow field. Comparisons of flow angle and secondary flow kinetic energy (SKE) agreed with previous studies and existing analytical methods, respectively. Collectively, these results indicate that tip clearance can be studied locally on an eccentric rotor.