R is GPL, so as long as you're complying with the GPL terms in your use of it or derivative works, you're fine. If you make your own API-compatible reimplementation of R that isn't covered under the GPL's permission grant, though, then you might have issues (this case will in part determine what kinds of issues).
Also, the copyrights for R are mainly held by the nonprofit R Foundation, not by Revolution Analytics: https://www.r-project.org/foundation/. An API case from R copyright holders would additionally be really messy because a huge portion of the APIs originate in Bell Labs S, which they don't own the copyright to. Though there might be some sleeper case where whoever now owns the original S copyright pops up and sues R users for having cloned S's API...