  We report a decaying kink oscillation of a flux rope during a confined
eruptive flare, observed off the solar limb by SDO/AIA, that lacked a
detectable white-light coronal mass ejection. The erupting flux rope underwent
kinking, rotation, and apparent leg-leg interaction during the event. The
oscillations were observed simultaneously in multiple AIA channels at 304, 171,
and 193 {\AA}, indicating that multithermal plasma was entrained in the rope.
After reaching the overlying loops in the active region, the flux rope
exhibited large-amplitude, decaying kink oscillations with an apparent initial
amplitude of 30 Mm, period of about 16 min, and decay time of about 17 min. We
interpret these oscillations as a fundamental standing kink mode of the flux
rope. The oscillation polarization has a clear vertical component, while the
departure of the detected waveform from a sinusoidal signal suggests that the
oscillation could be circularly or elliptically polarized. The estimated kink
speed is 1080 km/s, corresponding to an Alfv\'en speed of about 760 km/s. This
speed, together with the estimated electron density in the rope from our DEM
analysis, $n_e \approx$(1.5--2.0)$\times 10^9$cm$^{-3}$, yields a magnetic
field strength of about 15 G. To the best of our knowledge, decaying kink
oscillations of a flux rope with non-horizontal polarization during a confined
eruptive flare have not been reported before. These oscillations provide unique
opportunities for indirect measurements of the magnetic-field strength in
low-coronal flux ropes during failed eruptions.
