How about R-node ?
I think another alterative would be to use node.js as a server (http://nodejs.org/) and call R from within as a child process, search the Node.js API docs for specifics.
Note: node can run any JS script(s) you may have, they don't necessarily need to be node-specific.
If you're ok with having the R code run on a server, then you should take a look at OpenCPU. It provides a REST API and corresponding JavaScript library for sending R code to the server and getting the results back. In particular, it takes care of the security problems that can arise from running R as a server (R code can run arbitrary shell commands, among other things). There are public demo instances that you can use to try it out, and this page provides a simple tutorial.