I am a US citizen an my wife is a US permanent resident. We live in New Jersey. My wife has some family business in her native country. She is looking to bring some of that money via wire transfer to our account in the USA. Do we have to pay taxes on that money?

Did you declare that income on your joint return, because, as U.S. residents, ALL world-wide income is subject to U.S. income taxes.

While there are NO transfer taxes, the IRS WILL ask the source of the income and may determine that it should have been declared on your tax return.