To be clear, I understand your question to be primarily about grammar as it applies to pronunciation, not primarily about spelling, since you said "it sounds odd to me". There are certainly grammatical rules about the pronunciation of contractions, weak forms and other things that native English speakers often ignore or just think of as "lazy", "careless" or "sloppy" pronunciation. For example, Wilson left a comment mentioning the often-discussed linguistic fact that some speakers feel that they cannot use "wanna", or that "wanna" would sound odd, in sentences like "Who do you wanna win the game?", where the subject of the infinitive following "want to" is different from the subject of the verb "want" (the comment links to https://www.princeton.edu/~browning/wanna.html). (I said "some" because my impression is that there may be more variation between speakers in this area than is commonly acknowledged.)
"You can go if you wanna" sounds acceptable to me
Maybe some people feel differently, but for me, "wanna" (which I use as a written representation of a particular pronunciation of "want to"; something like [wɑnə] or [wɑɾ̃ə]—this is just an impressionistic transcription, not the result of rigorous phonetic analysis) can stand alone at the end of a sentence just as well as "want to".
Grant Goodall ("Contraction") seems to describe a few relevant examples, but unfortunately says we don't have very good data about their acceptability:
Pullum (1997) points out that in principle we should be able to look for such evidence by examining the behavior of wanna vs. want to in constructions where an overt element in T is required. VP ellipsis (as opposed to null complement anaphora) and VP fronting are two such constructions. Examples of the latter are given in (9).
(9) a. I said I'd wash the dishes, and wash them I did.
b. *I said I'd help wash the dishes, and wash them I helped.
If wanna involves no overt element in the embedded T, we would then
predict that (10b) would be worse than (10a).
(10) a. I said I'd feel like climbing the mountain, and climb it I want to.
b. I said I'd feel like climbing the mountain, and climb it I wanna.
Pullum reports that unfortunately, judgments on sentences like these are so
unclear and inconsistent to be of little use (and similar results obtain with examples involving VP ellipsis), so at this point it is an open question whether it is possible to find evidence for or against the presence of to in the clause embedded under wanna.
If I remember correctly, some linguists have analyzed the "particle" to that is used before infinitives in English as an auxiliary. If that analysis is correct, perhaps an analogous example would be the weak pronunciation of have in sentences like "You should have" (this weak pronunciation of "have" can be represented in writing as "You should've", which is an informal spelling but which I would say is not considered a misspelling, or as "You should of", which is fairly common in informal contexts, but commonly considered a misspelling).
That said, nohat♦'s answer to "Is there some rule against ending a sentence with the contraction “it's”?" quotes a section of the Cambridge Grammar of the English Language (Huddleston and Pullum, 2002) which apparently indicates that in the authors' judgement a strong form is needed in a similar sentence:
They want me to resign, but I don’t intend [to __].
I'm not sure how to explain the discrepancy between this and my judgement of sentences like "You can go if you wanna". It may be possible that to usually has a strong pronunciation in this context, but the contraction wanna is an established alternative to want to.
"Another Argument Against Wh-Trace" (Ivan A. Sag) seems to indicate that Pullum has in fact proposed that there is something special about wanna and similar words:
the arbitraryness of the set of verbs to which it applies: gonna, hafta, *intenna (intend to), *lufta (love to), *meanna (meant to). Indeed, as Pullum (1997) shows in detail, the optimal analysis of this entire class of verbs involves no rule of 'Wanna Contraction'—wanna forms are morphologically derived. The relevant morpholexical rule applies to seven verbs that select for a single infinitival complement; hence transitive want (which selects for two complements) has no such form. Pullum's analysis explains all phenomena previously discussed in the literature, as well as further data that serve to distinguish his proposal from others that have been advanced.
[...] Pullum, Geoffrey K. 1997. The Morpholexical Nature of English to-Contraction. Language 73: 79–102.
However, it seems Pullum's account has been criticized by Hans C. Boas ("You Wanna Consider a Constructional
Approach towards Wanna-contraction?", 2004).
The spelling "wanna" is often stigmatized in any context
Another entirely separate issue is the appropriateness in general of the spelling "wanna". As other people have mentioned, many people find the spellings "wanna" and "gonna" inappropriate in any context in any but the most informal writing (I would say it's most likely to be tolerated in online chat rooms or in fictional dialogue). It's never incorrect to write "want to" instead of "wanna", and it's unlikely that any reader will find the spelling "want to" to be overly formal, so you should advise your students to get out of the habit of writing "wanna".
Note that avoiding spellings like "wanna" and "gonna" doesn't necessarily mean that you should try to avoid the corresponding pronunciations: I use the pronunciation [wɑnə] or [wɑɾ̃ə] much more often than I use the spelling "wanna". Many English words and phrases have reduced pronunciations ("weak forms") that are not typically indicated in writing, and that native speakers may not even realize they are using. See the Language Log post Ask Language Log: Writing "gonna" or "going to" (Mark Liberman) for some more relevant information.