You can contribute to your IRA by cash, check or money order. That's it. You can't contribute property, not even gold coins or triple A bonds, and you can't make contributions on credit. If your card allows you to take a cash advance, you might be able to use that to make contributions, however.
You can't contribute a cash advance or anything else to your IRA if you're not earning compensation. Normally you can put up to $5,500 a year in your IRA, or $6,500 if you're 50 or older, but only if you've earned that much. If your earnings are only $3,000, $3,000 is all you can contribute. Employment and self-employment pay count as compensation, but income from rentals, dividends or Social Security doesn't qualify.
Even if taking a cash advance is an option, it's probably not the best choice. The interest rate on cash advances is typically higher than your regular credit card rate, and there's no grace period: as soon as you get the advance, the credit card company starts charging. On top of the interest, there's typically a 3 to 5 percent fee based on the amount of cash you took. Unless your IRA is earning a phenomenal return on your investment, contributions by cash advance will usually end up costing you money.
One way to put money in an IRA despite a low income is to make a rollover from another account. You can transfer assets from an underperforming IRA into a stronger one, or move your 401(k) into an IRA after you leave your job. Some companies allow you to roll over your workplace plan even before you leave your job. You can roll over pretty much any retirement account but a Roth into a traditional IRA.
If your money's tight this year, there's no obligation to make IRA payments, nor is there a penalty if you don't contribute. You don't need a credit card to tide you over to the next payment. If it's the convenience of credit card payments that you like, you can set up with your IRA custodian to pay online, or to arrange for automatic payments from a bank account. You can also contact the IRS to put this year's refund directly into your IRA.