Yes, your spouse who doesn’t work can open a Roth IRA. If you file a joint income tax return and at least one of you has taxable income, you can both contribute to your own separate Roth IRAs. But the IRS income-eligibility limits still apply.
Let’s say 40-year-old John makes $150,000 and his wife, Kate, stays home with their kids. John can put up to $7,000 in his IRA. And Kate can open a spousal IRA in her own name and contribute the maximum amount of $7,000 as well.