Superdiversity refers to large cultural diversity in a population due to immigration. In this paper, we introduce a superdiversity index based on the changes in the emotional content of words used by a multi-cultural community, compared to the standard language. To compute our index we use Twitter data and we develop an algorithm to extend a dictionary for lexicon-based sentiment analysis. We validate our index by comparing it with official immigration statistics available from the European Commission's Joint Research Center, through the D4I data challenge. We show that, in general, our measure correlates with immigration rates, at various geographical resolutions. Our method produces very good results across languages, being tested here both on English and Italian tweets. We argue that our index has predictive power in regions where exact data on immigration is not available, paving the way for a nowcasting model of immigration rates.