Yes, using the Latin and Cyrillic alphabet. However, I'm not sure if that answers the question you have in mind, or whether you are wondering about a homegrown phonetic system like Hangul.

First of all, there are the Dungan people. These were a Muslim minority in Shaanxi and Gansu who revolted during the 1860s and 70s. When the rebellion was put down by the Qing, large numbers of them fled to Imperial Russia (today's Kyrgyzstan and Kazakhstan).

The language they spoke/speak is close to the Gansu and Shaanxi Central Plains Mandarin. This spoken language was written in Xiaoerjing, a phonetic alphabet of Arabic origin. In the 1920s, the Soviet Union banned Arabic script, replacing it with a Latin script. Then, in 1940, this was once again replaced by a Cyrillic script.

Then there's the journey to hanyu pinyin. Soviet enthusiasm for the Latin script during the 1920s also affected China itself. In 1928, Russian scholars began development of Latinxua Sin Wenz (la ding hua xin wen zi, or, New Latin Script). This was adopted by the aforementioned Durgans, and also spread in China. It's worth mentioning that different forms of Latinxua Sin Wenz were developed for different forms/dialects of spoken Chinese.

The Latin script received support from several prominent Chinese, including Mao, who told an American journalist in 1936, "Sooner or later, we believe, we will have to abandon characters altogether if we are to create a new social culture in which the masses fully participate."

During the 2nd Sino-Japnese War and the civil war that followed, Latinisation was put on hold. When the communists formed the new government in 1949, the question of literacy once again came to the fore.

There were at least 3 tricky considerations to take into account.

First, you need literate people to teach literacy, and most literate people weren't literate in Latinxua Sin Wenz, they were literate in the "traditional" Chinese script.

Second, Chinese script contains a lot of information about meaning, and less information about pronunciation. So it's easy for various dialects to share a writing system. There are differences in syntax and vocabulary between dialects, but the fact remains that every written character can be given a pronunciation in any dialect.

This is the opposite of a phonetic alphabet, which contains a lot of information about pronunciation and less about meaning. So to move to a unified phonetic alphabet you need a unified pronunciation, and China didn't have one.

Third, the Chinese written characters at that time were complicated and difficult to learn.

(When Mao asked Stalin for his opinion, he advised Mao, "You’re a great country, and you should have your own Chinese alphabet. You shouldn’t simply use the Latin alphabet.")

The result of all that was threefold. The new government pushed putonghua (normal speech, or standard Mandarin) as a unifying language. It also developed a simplified version of Chinese characters (which are used in Singapore and China, while Taiwan continues to use "traditional" Chinese). Finally, there was a call for suggestions on a new writing system. Around 1,700 submissions were received, from which Mao finally picked 1 Latin based one, which was hanyu pinyin.