Is income required in order to make a contribution to a ROTH IRA?

Yes. Not just any kind of income, the IRS rules require "earned income". There are a lot of different ways to have "earned income", the most common of which is getting a paycheck. Note, dividends and interest are not earned income.

There are also other rules governing qualifications for contributing to a Roth. You can find them in the IRS Publication 590.

There is one way income is not required to contribute to a Roth. If you have no income, but your spouse does, you can qualify based upon your spouses income. The maximum you can contribute is a function of your earned income, your age (over 50 qualifies for a higher level) and the maximum set for that calendar year.