I was just reading online that some of the graduate programs for history often require to know the written language in a specific area of interest. When did you start learning that language in order to get accepted to a graduate program? I’ll be starting mandarin sophomore year as an undergrad, and I’m worried that by the time I’m done with school I won’t be ready to enter the next level of education.
History programs at the grad level do, in the US at least, usually require at least one non-English language and there is usually the expectation that you will acquire another language during your time as a PhD candidate. The reason for this is that there is very little history where the primary source documents are in English. If you cannot understand the language of the society that you are studying then you cannot do original research, you would be dependent on secondary sources only.
Since you are starting at the sophomore level you’re probably okay, two years of a language is usually what’s required. Look at the programs you might be interested in and their individual admissions requirements and build from there.
It is worth noting that full expressive fluency is not nearly as important as one might think — the important thing is to be conversant in the written language of your sources. If you are specializing in Bronze Age collapse, for example, you must be able to gloss Greek well and easily, but no one is expecting you to publish your papers in ancient Greek.
If your area of focus and interest is China, both a working knowledge of Classical Chinese and the ability to communicate with scholars in China will be prized, but if your interest was, say, mediæval Europe, an ability to read Latin and also communicate well at conferences in Romance languages would be useful, but no one would expect you to be communicating with foreign scholars in Latin.
If you develop a good working knowledge of one or more Chinese dialects (probably Mandarin would be the most popular choice, although someone interested in Chinese migration to the U.S. in the 19th century might prefer Cantonese, for example), it will certainly be beneficial, and one of the best ways to practice one's knowledge would be to work there for a year or two after undergrad in a non-English-speaking position.
There are immersion opportunities in a few places in the U.S. — Middlebury College in Vermont is probably the best known — but taking a Fulbright or simply a job overseas is probably one of your better opportunities to work on such a notoriously challenging language as Chinese.