What is the ruling regarding a man swearing to his new wife that he has no wife but her, while intending divorce by that oath?

If you falsely swore by Allah that you do not have a second wife, this is a "yamin ghamus" (a perjurious oath) and a major sin that necessitates sincere repentance. This oath does not constitute a divorce, even if you intended it to; because the wording does not imply separation, and intention only works with what resembles what you intended it with. It is incumbent upon the wife not to put her husband in such an embarrassing situation by demanding an oath, just as it is advised to beware of using divorce as a means to solve marital problems.