I discussed the evidence from the sixth and seventh centuries here. There's certainly a lot more to talk about from the earlier period, but unfortunately you will have to wait for someone else to turn up to provide an answer. The evidence is fragmentary, but contact undoubtedly existed, even if we cannot talk with any certainty about the exact nature of the relationship or how much either of the two powers knew of each other.

Rome and Ancient China Here is the section of the FAQ that deals with your question. If you have any more specific questions feel free to ask of course!