MRI has a rapidly growing role in radiation therapy (RT) for treatment planning, real-time image guidance, and beam gating (e.g., MRI-Linac). Free-breathing 4D-MRI is desirable in respiratory motion management for therapy. Moreover, high-quality 3D-MRIs without motion artifacts are needed to delineate lesions. Existing MRI methods require multiple scans with lengthy acquisition times or are limited by low spatial resolution, contrast, and signal-to-noise ratio. We developed a novel method to obtain motion-resolved 4D-MRIs and motion-integrated 3D-MRI reconstruction using a single rapid (35-45 s scan on a 0.35 T MRI-Linac. Golden-angle radial stack-of-stars MRI scans were acquired from a respiratory motion phantom and 12 healthy volunteers (n=12) on a 0.35 T MRI-Linac. A self-navigated method was employed to detect respiratory motion using 2000 (acquisition time=5-7 min) and the first 200 spokes (acquisition time=35-45 s). Multi-coil non-uniform fast Fourier transform (MCNUFFT), compressed sensing (CS), and deep-learning Phase2Phase (P2P) methods were employed to reconstruct motion-resolved 4D-MRI using 2000 spokes (MCNUFFT2000) and 200 spokes (CS200 and P2P200). Deformable motion vector fields (MVFs) were computed from the 4D-MRIs and used to reconstruct motion-corrected 3D-MRIs with the MOtion Transformation Integrated forward-Fourier (MOTIF) method. Image quality was evaluated quantitatively using the structural similarity index measure (SSIM) and the root mean square error (RMSE), and qualitatively in a blinded radiological review. Evaluation using the respiratory motion phantom experiment showed that the proposed method reversed the effects of motion blurring and restored edge sharpness. In the human study, P2P200 had smaller inaccuracy in MVFs estimation than CS200. P2P200 had significantly greater SSIMs (p<0.0001) and smaller RMSEs (p<0.001) than CS200 in motion-resolved 4D-MRI and motion-corrected 3D-MRI. The radiological review found that MOTIF 3D-MRIs using MCNUFFT2000 exhibited the highest image quality (scoring>8 out of 10), followed by P2P200 (scoring>5 out of 10), and then motion-uncorrected (scoring<3 out of 10) in sharpness, contrast, and artifact-freeness. We have successfully demonstrated a method for respiratory motion management for MRI-guided RT. The method integrated self-navigated respiratory motion detection, deep-learning P2P 4D-MRI reconstruction, and a motion integrated reconstruction (MOTIF) for 3D-MRI using a single rapid MRI scan (35-45 s) on a 0.35 T MRI-Linac system.