Not all graduate students will be eligible to contribute to an IRA because IRAs require “taxable compensation” (formerly known as “earned income”).
“Generally, compensation is what you earn from working” (source) and includes wages, salaries, and self-employment income, among other few other types of income. A few types of income that are not earned are rental income, interest and dividend income, and pension income.
At first blush, it would seem that graduate student pay would fall under wages or working for someone who pays you. However, that is only true for graduate student pay that is compensatory. Non-compensatory pay may not be eligible for IRA contributions. Publication 590 states that “scholarship and fellowship payments are compensation for IRA purposes only if shown in box 1 of Form W-2.” (See this explanation of how to calculate your taxable income for a discussion of compensatory and non-compensatory pay.)
The question of whether or not you can contribute to an IRA will come down to what kind of tax forms you receive in January. If you receive a W-2, you have taxable compensation and can contribute to an IRA from that income. If you receive a 1099-MISC with box 3 income, a 1098-T, a courtesy letter, or no notifications whatsoever, the form indicates that portion of your income is not eligible to contribute to an IRA.
Remember that you can contribute to an IRA up to your amount of taxable compensation for the year or $5,500, whichever is lower. If part of your income is compensation, you can contribute to an IRA from that portion – this may be the case if you switch funding sources between school years or between the academic year and the summer or if you have outside self-employment income. Also, if your spouse has taxable compensation, you can contribute to a Kay Bailey Hutchison spousal IRA (up to $11,000 between both IRAs).