The short answer is--yes, there are many tone languages that express certain kinds of questions (usually echo questions or yes-no questions) intonationally, and more often than not the intonational contour is in some sense "rising".
Before continuing it should be noted that there are documented cases of languages--tonal and non-tonal--that mark questions with an explicit intonational pattern that is not rising (see the related question referenced in the comments above: Intonation for questions in different languages and child's early language development intonations). I'll set those cases aside for the purposes of this question.
The long answer entails answering another question first: how do you define "rising intonation"? For example, for the intonation to be considered "rising", does the slope of the pitch contour at the end of the utterance have to be positive? Or is it sufficient for the more global trend of the utterance melody to shift upwards towards the end of the utterance?
If you adhere strictly to the former definition, Mandarin echo questions (which do not contain a final -ma particle) that end in tones other than Tone 4 (the falling tone) would fit the bill, but T4-final echo questions would not, since their final local slope is negative. In Cantonese, however, a relatively steeply positive final pitch slope is observed on all echo questions, independent of tone.
If, on the other hand, an overall upward shift of the pitch range towards the end of the utterance is the criterion, then Mandarin might qualify, regardless of the final lexical tone. It's been observed that the last syllable in the echo question is usually produced with an expanded pitch range. So, even in an echo question that ends in T4, the peak of the T4 contour is higher than it would have been in the declarative version of the utterance, and it is likely higher than the peaks of T4 contours earlier in the utterance (unless those syllables are being emphasized for some other reason).
Both types of behavior have been observed in tone languages from other parts of the world, including Africa. Also, sometimes a lack of declination over the course of the utterance (declination being the steady downward trend of the pitch range typical for "neutral" declarative utterances) is observed on intonational questions.