Yes, we know that the latest possible date for the first Roman to appear in China would have being 166 AD when Chinese sources records a delegation proclaiming themselves to be the ambassadors of King "Andun" (Antonius Pius) of "Da Qin" reached the Han capital of Lounyang. While in the 90s AD a Chinese general had dispatched his aide Gan Ying to the "western sea" and visit the kingdom of "Da Qin". Whether Gan Ying was indeed visiting Rome however is up for dispute.

If by 'Roman' you mean simply someone who was a citizen of the Roman empire, then yeah, there was a lot of travel back and forth. One group in which I'm interested in my own research are the Nestorians. After being condemned by two ecumenical councils in the 5th century, the Nestorians began looking East. They began to send missionaries as far as China. Indeed, we have a stele from 781 in Xi'an which was written by a Nestorian monk. It commemorates Christianity in the Tang dynasty.