As far as the law goes, you can be denied a visa for (almost) any or (almost) no reason, including if the consular officer doesn’t like the color of your tie.
Whether you will be denied a visa for having unpaid credit card debt is therefore not an objective science, but probably not. The consular officer’s task is to reject people who would attempt to immigrate illegally, overstay, or otherwise commit a crime if they were let into the US. Having unpaid debt is not a crime and is not immediately part of the consular officer’s remit.
If the consular officer somehow gets into his head that having unpaid debt somehow makes you more likely to overstay or commit crimes, you could in principle be rejected on that basis, with few or no ways to challenge that decision. But it doesn’t sound like something one would expect to happen.
Credit:stackoverflow.com‘