Notes for Lecture 1 reference the arrival of Shih Li-fang in 221 BCE, a missionary dispatched by Ashoka
(see page 14)
Ch'en, in his Buddhism in China, discredits this theory, stating that, "These attempts by Chinese Buddhists to find some connections with Asoka are understandable, but there is nothing in the Asokan inscriptions nor in the Ceylonese chronicles to indicate the slightest hint of Asoka's having propagated the religion in China." (see page 28)
Worth reading multiple sources on this.
Also note that Ch'en's overview of the introduction of Buddhism into China is concise yet detailed (so worth a full read). Read pages 27-46 at a minimum.
He also makes the case for the introduction of Buddhism in 2 BCE as documented in the Wei-Lueh.
Ashoka
Even though we might not have historical eveidences that Ashoka send any emissaries to China , we do know that he sent them to North West India , Kashimir and Gandhara region , so indirectly is responsable for the propagation of Buddhism not only into China but also all over Panasia .