Do I pay Zakat if I have a student loan?

Yes, you may be entitled to pay Zakat if you have a student loan. If you are not making any payments toward your loan right now, then there is nothing for you to deduct and you will simply pay Zakat on your net zakatable assets. 

If you are committed to a monthly repayment program toward your student loan, then you may deduct 12 month’s of upcoming principal payments (not interest). Example: you have $5000 in the bank. You pay $200 per month toward your student loan, of which $150 is toward the principal and $50 is interest. So, $150 x 12 months = $1800. This $1800 is your deductible. Your Net Zakatable assets are $5000 - $1800 = $3200. Zakat rate of 2.5% applied to $3200 = $80 Zakat due.

It should be noted here that if one has the ability to pay off an interest-bearing loan sooner than later and avoid as much interest as possible, then this is highly encouraged and a much greater priority than Zakat.