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Hi!
I am a rising junior and have to choose my major with the intention of pursuing law degree later.
Both are so interesting to study, but I have been worried too much if there were any harsh/irrational discrimination towards international students in the legal market. My native language isn't English, but would major in Applied Linguistics will necessarily cover up my Achilles heel when in admissions, job markets, and etc.? Because it demonstrates a better verbal proficiency?

What do you guys think?

Any discrimination would be towards students who are international students when they are in Law School. I don't know much about visas, but I would be surprised if you were able to get both an undergrad degree and a law degree on a student visa. From your post, I assume you are an international student as an undergrad, studying in the US.

Your major will not cover up any deficiency in English proficiency. People will judge your English on your resume, application, essays, and in interviews. The fact that you could easily choose either major is an example of why people don't judge English ability from your major--the two don't correlate.

In fact, if you were going to choose a major solely for this reason (which you shouldn't) I would advise that you major in sociology. Typically, sociology is far more reading and writing intensive than linguistics. Employers and law schools want to know that you can read and write well, not that you can describe the reading and writing of other people well.