Yes, but this sentence would most likely be used as an introduction (Oh, hi Mark here is my wife Rania). If you wanted to say My wife is Rania, most would add ' هِيَ ' which means she is. If you wanted to, for example, identify your wife from a list of names, you would say: "زَوْجَتي هِيَ رانْيا", which translates to My wife, she is Rania.
I agree that the version with هي makes it clearer. But without further context provided, زوجتي رانيا is equally translatable to "my wife is Rania" which should be accepted in my opinion. Duolingo's policy with other languages is that all possible translations are accepted and not only the most likely ones.
I agree, TimORiordan, and I think phuvtuo's remark about the lack of a full stop is unsatisfactory. Of course, the rules of punctuation dictate that a sentence must end in a full stop, but your question was not about punctuation; it was about whether those words COULD form a sentence, even without the addition of هِيَ .
Yeah, I didn't like that full stop argument either. But I have since observed that phuvtuo is, in fact, correct. (I would like to be able to put an emoji here of eyes rolling to heaven!!) Kudos to them. More sneakiness on the part of DuoLingo - not making that very clear! :-D