In this manuscript, to the best of our knowledge, we proposed the first optoelectronic oscillator (OEO) that can generate arbitrary microwave waveforms. A reconfigurable optical waveform generator is constructed via optical carrier-suppressed single-sideband modulation. The optical waveform from the generator can be seen as a series of frequency-scanning optical wavelengths in the frequency domain, and at any instant, the number of wavelengths can be from 0 to infinite. When the optical waveform serves as the optical source for an OEO based on the phase-modulation-to-intensity modulation conversion using a phase modulator cascaded with a phase-shifted fiber Bragg grating, a frequency-scanning microwave photonic filter with scanning characteristics according to the optical waveform is realized. By setting the period of the optical waveform or its multiple equal to the cavity round-trip time, a Fourier domain mode-locked (FDML) OEO that can generate arbitrary microwave waveform is realized. The key contribution of the work is that the concept of FDML OEO is further analyzed and extended to generate an arbitrary microwave waveform. Based on the proposed system, in addition to the single-frequency microwave signal and linearly-chirped microwave waveforms, low phase noise arbitrary microwave waveforms can be generated utilizing the low phase noise merit of an OEO.