They are both correct, though I'd probably use the second one, personally.
The past perfect form ("had resigned") emphasizes that resigning came first. In some sentences, it might be unclear which action happened first (or if they happened at the same time), though especially when using "as soon as", it's pretty clear which one is first. For "A as soon as B", B happens a very small time before A, so we don't really need more information to make that clear.
An example of where the meaning would change is when we use a less clear time phrase, like "around".
She got married around the time she resigned. (Before or after)
She got married around the time she had resigned. (probably after)