Sigma 10-20

Can A sigma 10-20 be used on a FF or just on 1.6X crop like the Canon 10-22

It can be used on FF but there will be poor border IQ and significant vignetting. The center 63% of the image will be the same quality as if you were using a 1.6 crop camera.
So you would end up with the crop FOV, after you cropped it PP.
Sigmas 12-24 would be a better choice, or perhaps a 14mm prime.

It has an EF mount, so will physically fit on a full frame camera, but the image circle is only big enough for aps sensors, so it will give bad results on FF.