No, unfortunately only Interest Paid is a tax deduction.
They charge interest, add it to your Loan Balance, then start charging Interest on the New Loan Balance. This is why student loan balances can double and triple in only a few years, especially if you're on a Deferred or Income Adjusted payment plan.
These are the only types of consumer loans allowed to do this.
Be sure to deduct any Education Expenses you paid with your Student Loans, as you may qualify for Education Credits.