We use the Iocco et al. (2015) compilation of 2,780 circular velocity measurements to analyze the Milky Way rotation curve. We find that the error bars for individual measurements are non-gaussian, and hence instead derive median statistics binned central circular velocity values and error bars from these data. We use these median statistics central values and error bars to fit the data to simple, few parameter, rotation curve functions. These simple functions are unable to adequately capture the significant small scale spatial structure in these data and so provide poor fits. We introduce and use the Gaussian Processes (GP) method to capture this small scale structure and use it to derive Milky Way rotation curves from the binned median statistics circular velocity data. The GP method rotation curves have significant small-scale spatial structure superimposed on a broad rise to galactocentric radius $Rapprox7$ kpc and a decline at larger $R$. We use the GP method median statistics rotation curve to measure the Oort $A$ and $B$ constants and other characteristic rotation curve quantities. We study correlations in the residual circular velocities (relative to the GP method rotation curve). Along with other evidence for azimuthal asymmetry of the Milky Way circular rotation velocity field, we find that larger residual circular velocities seem to favor parts of spiral arms.
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