What difference would starting an IRA do for my refund

You must actually contribute to an IRA to get a deduction on your tax return.

You have until April 15th to make a contribution for 2016. Make sure the custodian knows which year you want.

What would it do? A Traditional IRA contribution could reduce your tax liability  by the amount of the contribution  (if you have any tax liability).   It is not a refund, but only can lower the tax depending on what tax bracket you are in.   If you have no tax liability then it will not change your tax refund.  (A tax liability is what is left to be taxable income after all exemptions and deductions have been subtracted.)