I'm an independent contractor who had no jobs in 2016. Can I still file as self-employed and take advantage of business deductions?

Regardless of the business income, or even the total lack thereof, as far as the IRS is concerned, you are "in business" until you report the sale, closure or other disposal of that business. So until you do that, the IRS expects a SCH C from you, even if you have no income for the entire year.

Do understand however, that while you will still claim your business expenses and deductions, they will not be allowed since you have no business income to deduct them from. But they will be carried over to next year and deducted then, provided of course you have the business income in 2017 from which to deduct them. But if you don't claim them on the 2016 SCH C, then you can not carry them over to next year.