Technically, there is no Chinese ethnicity. China is made up of (officially) 56 ethnicities. My parents are ethnically Han Chinese. I was born in Canada, raised in America. I carry an American passport. To my neighbors, I'm a 华侨 (overseas Chinese); one taxi driver told me that I would be Chinese forever because it's in my blood. So what am I? Moving from the questions of ethnicity, is it possible for a foreigner to immigrate to China and become a Chinese citizen? I suspect the answer is 'no' but I have heard (perhaps from the internet) that one can become a citizen at the invitation of the Chinese government. It seems, being Chinese has more to do with ethnicity AND culture than anything else.
While some may deride China for being parochial/uncosmopolitan for this, many countries share this same trait: the majority ethnicity defines citizenship and acceptance. The United States isn't immune from this. Even though I grew up an American (and still consider myself American) I have experienced personal bias and prejudice because of my ethnicity. I got comments from kids about me going to Buddhist church (I'm not Buddhist), using karate in a fight (I don't know any form of martial arts), using chopsticks (this is true), or speaking "Ching chong, ching chong" (I am not familiar with this language). High school was hard. Not that it wasn't for any of my white friends who shared the same weight/height/car/popularity class as me, but none of them were ever told to "Go home."
The big "but" here is that I live/lived in the United States. And though there is a history of disenfranchisement as well as evidence of racial bias today, I am more hopeful that you (whoever you are) /can/ become American... not by becoming 'white', but by participating in a society that has the opportunity to change itself as well as the opportunity to change you.
It's not clear to me that this is possible in China (i.e. social change to embrace differing ethnicities). The average Chinese (pick any of the Chinese ethnicities) person has very strong feelings about one's identity as it relates to race and language (e.g. some people couldn't believe I was Chinese and couldn't speak Mandarin when I first got to China). In my first trip to China, I made a friend who relayed me this interesting anecdote (this was the late 90's): he (an American) was on a college campus and he engaged in a discussion about race relations in America with a Chinese student. The Chinese student told him: "There is no racism in China because there aren't any black people." While the ethnic tensions aren't as visible here, simply ask a Han person how they feel about Uyghers.