The Chinese dynastic history the Book of Later Han notes one instance of direct contact, but as you will see there is some ambiguity in what actually took place:

“In Emperor Huan's the 9th Year of Yanxi [166 AD], the King of Da Qin (“Great Qin”), Andun, dispatched envoys from beyond the frontiers through Rinan offering elephant tusks, rhinoceros horn and turtle shell. This was the first time there was communication. The tribute brought was neither precious nor rare, therefore raising suspicions that the accounts might have been exaggerated.”

Rinan was the Han empire's furtherest outpost on the south-west coast, located in modern northern Vietnam.

Da Qin was the westernmost country known to the ancient Chinese, located beyond Anxi (Parthia) and has plausibly been identified as the Roman world. The descriptions of Da Qin is a mix of plausible items (the products of Da Qin are said to include among other things coral, amber, glass, and gold-thread embroideries) to the more bizarre: (“The seat of government is more than [40 km] around. In this city are five palaces each [4 km] from the other. Moreover, in the rooms of the palace the pillars and the tableware are really made of crystal. The king goes each day to one of the palaces to deal with business. After five days, he has visited them all.”)

It is likely that the descriptions of Da Qin have been coloured by religious ideas of an utopian “Counter-China” in the furthest west. (“The people of [Da Qin] are all tall and honest. They resemble the people of the Central States and that is why this state is called Da Qin.”)

In the 160s the Roman Empire was ruled by Marcus Aurelius Antoninus, naturally people have identified him as King Andun of Da Qin. (I should note that finding the “original” behind a foreign name recorded in Chinese sources is a non-trivial task, you have to take into account the difficulties in fitting Indo-European consonant clusters into the Chinese script and the massive sound changes in the Chinese language since ancient times.)

One possible interpretation is therefore that in 166 an official embassy arrived in China from Emperor Marcus Aurelius of Rome. However this is probably the least likely explanation. As noted, the Chinese were not particularly impressed by the gifts offered, which were rather ordinary South-East Asian luxury goods rather than the sort of wondrous exotics they had expected.

The embassy might not have been made up of official envoys at all, but merchants or other private travellers claiming to be envoys to gain an audience and presenting as tribute trade goods they had acquired on their journey.

The delegation might not even have been made up of Romans. If some Persian or Bactrian con-man shows up at the Chinese capital claiming to be an envoy from far-away Da Qin, who is there to prove him otherwise?

TDLR: Chinese sources record the arrival in 166 AD of envoys from Da Qin, thought to be the Roman Empire. However there is no way of proving this was an actual official embassy or even that any of them were genuine Romans.