Can "I wonder" be put at the end of a sentence?

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?

Solution 1:

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.

Solution 2:

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."