In this paper, a new class of efficient angular chirp-Fourier transform (EACFT) algorithms are proposed to realize the fast detection and parameter estimation of chirp signal. The angular chirp-Fourier transform (ACFT) is first introduced to overcome the disadvantages of chirp-Fourier transform (CFT) and fractional Fourier transform (FRFT). Similar to FRFT, ACFT is also a time-frequency rotation operator. We derive the analytic relations between the length of time-frequency line and the width of spectral support (WSS) in the ACFT domain. Exploiting the time-frequency rotation property of ACFT, the EACFT is then proposed to detect the chirp signal and estimate its parameters. The EACFT can achieve high estimation accuracy only with two selected rotation angles instead of traditional traversal search, which largely reduces the computational cost. Based on the concept of EACFT, robust methods, i.e., morphology filtering-EACFT (MF-EACFT) and spectrum smoothing-EACFT (SS-EACFT), are further proposed to improve the applicability of EACFT in the low signal-to-noise ratio (SNR) and multi-component circumstances, respectively. Finally, the application of EACFT to the high-speed maneuvering target detection is developed. A new fast detection algorithm based on adjacent cross correlation function (ACCF) and SS-MF-EACFT is presented. Theoretical analysis and simulated experiments demonstrate the effectiveness of the proposed method.