This letter investigates the circularity of fractional Fourier transform (FRFT) coefficients containing noise only, and proves that all coefficients coming from white Gaussian noise are circular via the discrete FRFT. In order to use the spectrum kurtosis (SK) as a Gaussian test to check if linear frequency modulation (LFM) signals are present in a set of FRFT points, the effect of the noncircularity of Gaussian variables upon the SK of FRFT coefficients is studied. The SK of the α th-order FRFT coefficients for LFM signals embedded in a white Gaussian noise is also derived in this letter. Finally the signal detection algorithm based on FRFT and SK is proposed. The effectiveness and robustness of this algorithm are evaluated via simulations under lower SNR and weaker components.