I'm retired and drawing Social Security. Can I contribute part of my Social Security benefits to a Roth IRA account?

Nope. Sorry. To make a Roth IRA contribution, you must have earned income. Earned income is generally income you receive from working -- as compensation for your labor in one form or another. It's reported to you on a W-2 form, or you report it on Schedule C (Business Income) or Schedule F (Farm Income) with your normal tax return. Earned income generally does not include Social Security benefits, pensions, interest, dividends, rental income, or capital gains. It can, however, include alimony.