Two points: firstly, it should be called rebirth within a Buddhist context, because reincarnation involves a soul, which non-heretical Buddhism rejects.

Secondly, Bodhidharma was not the first Buddhist missionary to China, nor was he in a non-Buddhist society. Buddhist missionaries had been coming to China since at least the 2nd century CE (An Shiguo, for example), and achieved social and political prominence starting during the 4th century (Shi Le, the most powerful ruler during the 330s, was ably advised by the Serindian Kuchan Monk-Missionary Fotudeng). By the 5th century, there were substantial translations of Buddhist texts into Chinese with state support; most notably, the Serindian translator Kumarajiva, who was financed by the second emperor of Later Qin (後秦).

In this context of increasing popularization of Buddhism in China, rebirth was, as an integral part of traditional Buddhism, not new to China. Indeed, the story goes that Bodhidharma was introduced to the 6th century Emperor Wu of Liang, who is known as perhaps the most devout Buddhist Chinese Emperor. Wu, tellingly, is not reported to have asked for an explanation of rebirth, but rather how much merit he had gained through his support for Buddhism. Bodhidharma's new teaching was that all of the works were useless unless one practised Buddhist meditation according to his style.

So, no, Bodhidharma did not, even according to traditional Buddhist hagiography, introduce rebirth to China. He introduced other aspects of Buddhism to China, however, such as meditation techniques.