Since its invention in 1921 by Hull, magnetrons have undergone rapid development, transitioning from low-power devices to high-power relativistic magnetrons (RMs). However, research on RMs has been predominantly confined to L-X bands until now. To explore the potential of RM in higher frequency bands and align with the trend toward miniaturization of high-power microwave sources, a Ku-band RM has been investigated in this paper. Theoretical analysis dictates the selection of 24 cavities for optimal performance at a low magnetic field. Utilizing a three-dimensional particle-in-cell simulation platform, we demonstrate that the RM can generate a microwave power of 116 MW at a resonant frequency of 13.717 GHz with an electron beam of 126 kV and 2.0 kA, under a magnetic field of 0.22 T, corresponding to a power conversion efficiency of 46%. The integration of a modified all-cavity axial extraction structure in the Ku-band RM allows for a minimized inner radius of the magnetic field system to approximately 25 mm, while maintaining a high-power microwave output.