Jupyter Notebooks are web applications that allow you to create and share documents containing interactive code (so you can execute the code in the cell directly), write text, equations and visualizations. You insert code blocks as "cells" into the notebook.
You can use R in Jupyter notebooks. Get up and running following the instructions here
MyBinder.org will natively support Python only, but because it is based on Docker, it will install and run pretty much anything
You need to include a Docker file and an R script that installs the jupyter kernel in your github repo, like this one. However, it appears that it does not support the R kernel any longer. See the hosted notebook here (but you cant interact with it). Hopefully they'll fix this soon
Then I discovered SageMath Cloud. I created a free account, created a project, uploaded my ipynb file, and shared with the world!! Unfortunately it looks as if you need to create an account to run it interactively (rather than just view it). You create a project, create new file, paste the link, and hit the button 'download from internet'
I'd be interested to hear about any other free public hosting solutions for R jupyter notebooks!