Can I open a Roth IRA if I'm over 65?

You cannot contribute more to your IRA than the amount of your "compensation income." Compensation income is the taxable portion of your wages/salary, net self-employment, and alimony. Any amount shown in box 1 of a W-2 minus the amount shown in box 11 of the same W-2 is automatically considered taxable compensation income.

So if you are not doing some kind of work or receiving alimony, you can't contribute.

There is no age limit for contributions to a Roth IRA. People over 70 1/2 cannot contribute to a traditional IRA.