From a strictly mathematical perspective, you should fund the Roth IRA so long as you can fully pay off the CC by August.
Of course, this requires you to be reasonably certain that you can pay it off by August.
BUT, you can always pull out contributions from a Roth IRA tax and penalty free at any time. Meaning you can just fund the Roth, and if you come up a bit short in paying off your CC by August, just withdraw from the Roth.
This also assumes that whatever you invest the Roth money in won't lose a significant amount of value by August. If you want to be super safe, just park it in a money market fund until August, and then if you don't need it just switch it to an investment that you actually wanted.
The more confident you are that you'll be able to pay off this CC by August, the riskier an investment you can make in the Roth.
EDIT: But also, what tax bracket are you in? Does using a Roth actually make sense?