Not at the airport. You could google the nearest Service Canada in the city your will be landing and travel to that place from airport. You will be given a paper number and then the sin will be sent to your address later.
Just to know, why do you want to do it at airport, do you have a place for it to mailed to you. Recently the Service canada program for processing SIN had some fault on 3 may and now to get a sin the time line has been changed from 10 days to 30 days.