In such a huge continent and with so much talent to choose from, you can never give a complete answer to that question. However, there have been a number of 'top 10' and other lists. Most of these are lists of personal favourites, and nobody is saying they are definitive, but if you type 'best asian actors' in a search engine you will find several examples which may interest you.

For a more historical list, you could look at the CNN selection, which includes performers from the silent filme era and is headed by Zhou Xun, especially well known for her performance in Suzhou River. However, the makers of this list admit that they are quite biased and it's not to be taken seriously. Other lists concentrate on Asian actors in Hollywood, or the US generally - like this one which puts Ken Leung at the head.

You can also find lists by nationality - if you type 'best Indian actor (or whatever country you are interested in) you will get a more detailed answer.