Usually sentences with "I wonder" are of the following form:
I wonder why _______.
But what about this?
Why is it that _______ I wonder.
It seems relatively unnatural. Why is that? Is it grammatically correct?
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Yes you can, there's no rule against it. Usually it's preceded by a comma:
Why is it that [...], I wonder.
or like this example taken from here, after direct speech:
‘What should I do now?’ she wondered.
This kind of sentence-ending question may also be a rhetorical figure known as aporia (second entry on the linked page):
aporia [əˈpɔːrɪə] n 1. ... Rhetoric a doubt, real or professed, about what to do or say
It can also be construed as a sentence adverb (also "sentential adverb") which is "an adverb or adverbial phrase that expresses a writer's or speaker's attitude to the content of the sentence in which it occurs."