Learn English – Can “I wonder” be put at the end of a sentence

No, it cannot. The only instances the Oxford English Dictionary gives of the transitive use of wonder are obsolete.

As @Mitch comments, whilst it's relatively common in casual speech, I wonder shouldn't really be followed by an actual question (an interrogative).

Taking a typical interrogative, such as who are you, I don't know the specific grammatical term for the reordered version who you are, so I'll just call it a "wh- noun phrase" (which is what you should use after I wonder). Here's the relevant definition for wonder from OED...

(definition #2) Usually with clause: To ask oneself in wonderment; to feel some doubt or curiosity (how, whether, why, etc.); to be desirous to know or learn.

It's particularly worth noting the following supplementary point made by OED...

I wonder is often placed after a question which expresses the object of curiosity or doubt;
e.g. ‘How can that be, I wonder?’ = I wonder how that can be.

...where I've highlighted the word-order switch made in that example.