For completeness, the answer is: you can't do that from within RStudio. @agstudy has it right - you need to install the newer version of R, then restart RStudio and it will automagically use the new version, as @Brandon noted.

It would be great if there was an update.R() function, analogous to the install.packages() function or the update.packages(function).

So, in order to install R,

1. go to ,
2. click on 'CRAN',
3. then choose the CRAN site that you like. I like Kansas: .
4. click on 'Download R for XXX' [where XXX is your operating system]
5. follow the installation procedure for your operating system
6. restart RStudio
7. rejoice