Answer:
No. If you did not pay any taxes or have them deducted from your paycheck, you can not get a refund.
However, because of many special programs in the tax system, the earned income tax c credit programs most noteably, you may receive what would seem like a "refund" of taxes that you didn't even pay! These same credits may be provided over the year in each of your paychecks and you should talk with your payroll manager about it.