The answer is yes, but one cannot contribute directly to a ROTH

One cannot contribute directly to a ROTH IRA. One needs to contribute to a traditional IRA account first and then coverts the amount from the traditional IRA account to one's ROTH IRA account. 

It it possible that your income level is high enough so your contribution to the traditional IRA became nondeductible IRA. Therefore, you pay taxes on that portion of the IRA. When one converts it, one does not need to pay any taxes on that portion for which income taxes has already being paid.