It depends on the antenna nature. For example, a patch antenna can be excited on two orthogonal edges with a 90 degree phase shift to get CP. Two orthogonal dipoles excited with 90 degrees phase shift can also generate a CP. In other antennas, adding a slot in the antenna can generate a circular current on the antenna surface and yeild it CP. This is the case of a patch antenna with an L-shaped slot for exampe.
You need to make best efforts to make reception orthogonal, then residual non-orthogonality components (which will no doubt exist) you'll need to take out will a calibration. In the calibration you'll launch and measure co and cross-polarisations.