Every job I've ever had asks for a SS#. It's normal, don't worry.
Most companies ask for your social security number on their employment applications.
You MUST comply.
ANY job that pays you MUST report what you get paid to the federal AND state government, and you WILL have to fiel; taxes next year -- although you will probably get a refund.
ALL taxes are keyed off of yoru SSN#
Requires by laws.
Do not put on, applications is trashed.