Did you have any income earned from working? In order to put money into a Roth, you have to have income that you earned. A tax refund is not earned income.
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To make any contribution to an IRA, you must have compensation. Normally, this means either self-employment on a schedule C, or wages on a W-2.
If you have compensation, then it doesn't matter where a specific dollar came from. The tax refund goes into your bank account, it gets mixed up with all your other money and loses its identity, it's just money no matter where it came from. And you can take money out to contribute to the IRA, as mentioned, it doesn't matter where it comes from and money doesn't actually have an identity once you have it.
But if you don't have compensation, you can't contribute to any IRA, no matter what other sources of income you might have.
Under very limited circumstances, a tax refund may be considered "income". But. it is not earned income ("compensation") for the purpose of being eligible to make an IRA contribution.