Can Texas law garnish your bank accounts if you default on a credit card?

You've left out a lot of detail here. First, is this a joint account or just his? Second, is is SSI disability that he's receiving? Third, is that the ONLY source of income in his account? Fourth, was the card debt incurred for items used by both of you? Normally, if the only source of income is disability, then that cannot be levied from a bank account. But, a lot more detail is needed to make a complete analysis.

Mr. Corbin is correct that a lot more detail is needed to answer your question. Most fundamentally, is there a judgment that that the creditor has already obtained? Without a judgment, or at least filing a lawsuit and getting a prejudgment writ of garnishment, the credit card company cannot garnish a bank account, regardless of anything else. So the point here is if the credit card company hasn't sued you, you don't have to worry about garnishment. If the credit card company does sue, you may have to worry about it, depending on the answers to the various issues Mr. Corbin raised.