We have used the Josephson arbitrary waveform synthesizer (JAWS) to provide traceability for the phase of the harmonics, relative to their fundamental frequency, of a distorted waveform. For distorted waveforms with rms values from 0.154 to 0.2 V and harmonic magnitudes from 5% to 40% of the fundamental, our system can generate odd harmonics up to the 39th with best phase uncertainties from 0.001° to 0.010° (k = 2.0), depending on the harmonic number and harmonic magnitude. We anticipate that the ability of the JAWS to generate distorted waveforms with the lowest possible uncertainty in the magnitude, and phase spectra will make it a unique tool for low-frequency spectrum analysis.