I have never heard anything about Melatonin being in any way related to or an effective treatment for anxiety.

In most cases it's just meant to be a sleeping aide.

Now it could be the case that if it increases length/quality of sleep that may indirectly reduce anxiety and sleep deprivation can have a worsening effect over it.

But otherwise no, it's not something that should be taken with any expectation that it would help with anxiety directly.