The answer depends on what you consider to be part of your "project" – regardless, if you're using the IDE, it's almost always a good idea to have an .Rproj going. See the "Using Projects" from RStudio Support, below:
That doesn't mean you can just copy and paste that file and that all the data will come with you, though — you'd need those files as well.
Take a look at Jenny Bryan's post here: