Although optical aperture synthesis has been generally regarded as the only access to very large imager for over a century, the problem of phasing all the giant sub-apertures on the scale of wavelength is still prohibitive. Besides, the accompanied adaptive optics combatting the atmospheric turbulence is also bulky and complicated. We here propose a new paradigm aperture synthesis imager through turbulence, based on computational ghost imaging method. The complex aberrations on the signal path are computationally cancelled by introducing an optimum compensation phase on the reference path. With the advanced aberration cancellation, our imager is free from phasing and aberrations problem. The image degradation due to turbulence is also suppressed and even eliminated without any guide star or wavefront shaping device. Experimentally, diffraction-limited imaging is achieved under turbulence featuring transverse coherence length far less than the optical aperture of the system.