Traditionally, beamforming using fractional Fourier transform (FrFT) involves a trial-and-error based FrFT order selec-tion which is impractical. A new numerical order selection scheme is presented based on fractional power spectra (FrFT moment) of the linear chirp signal. This method can adaptively determinethe optimum FrFT order by maximizing the second-order central FrFT moment. This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably. This improves the mean square error minimization beamformer by re-ducing effectively the signal-noise cross terms due to the finite data length de-correlation operation. Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.