Distinction of orthogonal frequency-division multiplexing (OFDM) signals from single-carrier signals is highly important for adaptive receiver algorithms and signal identification applications. OFDM signals exhibit Gaussian characteristics in the time domain, and fourth-order cumulants of Gaussian distributed signals vanish, in contrast to the cumulants of other signals. Thus, fourth-order cumulants can be utilized for OFDM signal identification. In this paper, first, formulations of the estimates of the fourth-order cumulants for OFDM signals are provided. Then, it is shown that these estimates are significantly affected by wireless channel impairments, frequency offset, phase offset, and sampling mismatch. To overcome these problems, a general chi-square constant false-alarm rate Gaussianity test, which employs estimates of cumulants and their covariances, is adapted to the specific case of wireless OFDM signals. Estimation of the covariance matrix of the fourth-order cumulants is greatly simplified, peculiar to the OFDM signals. A measurement setup is developed to analyze the performance of the identification method and for comparison purposes. A parametric measurement analysis is provided, depending on modulation order, signal-to-noise ratio, number of symbols, and degree of freedom of the underlying test. The proposed method outperforms statistical tests that are based on fixed thresholds or empirical values, whereas the a priori information requirement and complexity of the proposed method are lower than the coherent identification techniques.