The orbital angular momentum (OAM) of beams provides an additional degree of freedom and has been applied in various scientific and technological fields. Accurate and quantitative measurement of intensity distributions across different OAM modes, referred to as the OAM spectrum of a beam, is crucial. Here, we propose a straightforward and efficient experimental setup for measuring the OAM spectrum of a randomly fluctuating beam. By employing a modal decomposition analyzer, a randomly fluctuating light field can be decomposed into an incoherent superposition of a series of modes, followed by a coordinate transformation to calculate the OAM spectrum. This method is suitable for measuring the OAM spectrum of partially coherent beams and superposition of vortex beams. The experimental results are in good agreement with the theoretical predictions. Precise measurement of the OAM spectrum is critical for various applications in optical communications, quantum optics, and digital imaging.