[Tsuwabuki]

No, you don't. Chinese is written entirely with Kanji. In fact 漢字 means "Chinese Character." Not only are there people who do study 漢字 without knowing hiragana, there are people who use a method of study where they don't even learn kun-yomi or on-yomi, but just ei-yomi: that is, they do not learn the Japanese native sound nor the sound based on the Chinese reading, but just the English meaning.

Without hiragana though, you will unable to understand conjugations, particles, as well as many common or less common words that are usually written such, even if they do have kanji. I do not recommend learning kanji by itself, nor do I recommend any regimen of Japanese language usage without kanji. The best is to study them together, practicing handwriting (shuji) by actually writing entire sentences, using kanji as needed for nouns or verb stems.