If I am applying for a job online or in person, what happens if I use my ITIN in place of the social security field?

Also, if I do that just for the sake of the application, can I use the ITIN as if it were a social security for taxes deductions on the paycheck?

In other words, will the employer know and will it make any difference?

Summer is here and I really need a job but the place where I live pretty much requires a social by default. I really don't want to take a manual labor type of job, which is the only ones that don't look into it.

Thanks everyone!!!