To accurately predict the acoustic radiation of rotating sound field, a prediction method of Kirchhoff rotating sound field is proposed. Based on the acoustic radiation of rotating point sound source, using spherical harmonics, Legendre function and dipole geometry, the frequency domain analytical expressions of acoustic radiation of rotating transverse and longitudinal dipole sources are constructed. The contributions of transverse and longitudinal dipole sources to acoustic radiation of rotating sound field are quantified. By introducing Kirchhoff integral and combining rotating point source with dipole source, the rotating Kirchhoff source is constructed. The mathematical model of acoustic radiation prediction of rotating Kirchhoff source and its analytical expression of sound pressure are derived. The key factors influencing its cutoff threshold for analyzing infinite harmonic order truncation are determined. Through numerical simulation, the effects of fundamental frequency, rotation frequency and rotation radius on the rotating sound field are discussed when Ma<1. The spatial distribution of sound pressure, Doppler and directivity characteristics of the rotating sound field are analyzed. The validity of the rotated Kirchhoff source is verified by the equivalence verification of the sound field, with a relative error of the sound pressure value at any arbitrary point being within 0.05, which further demonstrates the effectiveness of the rotating Kirchhoff source. The results obtained from experimental testing in a semi-anechoic chamber confirm the effectiveness and accuracy of the Kirchhoff integral method, consistent with the simulations. This method effectively improves the prediction accuracy of the rotating sound radiation by replacing the traditional point source superposition with the constructed rotating Kirchhoff source. These research findings hold significant theoretical reference value and significance for the control of rotating machinery radiation noise and the design of low-noise rotation structures.