Hi there, I am a student currently studying in china with a temporary resident permit.

Hi, you can try to convert your current student X type to the dependant visa at the exit and entry administration of the local PSB within China. If it can be done, there is no need to leave China.
You need to provide the relevant documents including your passport and its copy, the application form, a passport-style photo, valid registration form of temporary residence, marriage certificate, an invitation letter from your wife, copies of your wife's passport and residence permit in China. Then, go to the local PSB to submit the application.