Polygamy is not acceptable as per US law. the people who are already married and want to marry again to a US citizen have to finish the previous relation otherwise they will simply rejected by US visa authorities.
US visa authorities will severely check your matrimonial background prior to issue you a US marriage visa. Here, the example of a Syrian man can be taken into account that was already married and marry again to a US citizen. But his visa was declined due to the reason of polygamy. Even though he divorced his previous wife at a later stage but he was refused to enter in USA because polygamy is a serious offense under US laws and US visa authorities do not allow such a person to enter in USA who has been involved in polygamy.
