We consider a phase-shift mixing model for linear sensor arrays in the context of blind source extraction. We derive a blind Capon beamformer that seeks the direction where the output is independent of the other signals in the mixture. The algorithm is based on Independent Component Extraction and imposes an orthogonal constraint, thanks to which it optimizes only one real-valued parameter related to the angle of arrival. The Cramér-Rao lower bound for the mean interference-to-signal ratio is derived. The algorithm and the bound are compared with conventional blind and direction-of-arrival estimation+beamforming methods, showing improvements in terms of extraction accuracy. An application is demonstrated in frequency-domain speaker extraction in a low-reverberation room.