There is no law to stop non-native speakers working as English teachers in China, and it has been done. However, the experience of many non-natives who have tried this is that it is very difficult to find work, and you are more likely to succeed if you have some specialist knowledge (for example, a degree in a subject where teachers are needed) or contacts who can help you. Most countries prefer native speakers to teach specific languages anyway, and this is also true of China. However, it is also a very large country with a great many people who want to learn English, so a well qualified teacher should find opportunities. There is a lively discussion on this topic here.
The best way to find work is to approach a reliable agency, or ask a China based company such as English First. They will give you an honest answer and suggest ways to look for work.