Abstract: The existence of non-random galaxy intrinsic ellipticity severely challenges precision cosmic shear measurement. We propose to self calibrate the induced cosmic shear-galaxy intrinsic ellipticity contamination (the GI correlation, Hirata04b) using extra information encoded in the same weak lensing survey. Besides the galaxy ellipticity-galaxy ellipticity correlation, the same lensing survey also measures the galaxy ellipticity-galaxy density and galaxy density-galaxy density correlations. These extra correlations allow the measure of the intrinsic ellipticity-galaxy correlation, which links to the GI correlation in a rather model independent and predictable way. Our self calibration technique is applicable to all weak lensing surveys with photometric redshift information. After the self calibration, the residual systematical error is usually a factor of 10 smaller and the residual statistical error is usually below the statistical limit of cosmic shear measurement. The self calibration technique also sheds light on correcting the intrinsic ellipticity-intrinsic ellipticity contamination.