Abstract: Vortex electromagnetic waves (VEMW) carrying orbital angular momentum (OAM) possess unique multi-modal orthogonality and helical wavefronts, providing conditions for novel inverse synthetic aperture radar (ISAR) imaging. However, the inherent complex phase modulation of VEMW coupled with phase errors induced by maneuvering targets renders conventional imaging algorithms incapable of accurately decoupling target information from echoes. To address this challenge, this paper proposes an imaging method integrating Fractional Fourier Transform (FrFT) and Fourier Ptychographic Microscopy algorithm (FPM). First, a vortex ISAR maneuvering targets imaging model is constructed with pre-compensation applied to the Bessel function term and Azimuth angle term. Subsequently, range compression is performed on the echo signal via FrFT to obtain a focused range image. Finally, the FPM algorithm utilizes targets intensity information to iteratively reconstruct the spectrum in alternating spatial and frequency domains, thereby recovering phase errors. Simulation results demonstrate that the proposed method can effectively recover phase errors and generate focused vortex ISAR images under low signal-to-noise ratio (SNR) and non-cooperative maneuvering scenarios.