Don't use Rstudio to update R. Rstudio IS NOT R, Rstudio is just an IDE. This answer is a summary of previous answers for different OS. For all OS it is convenient to have a look in advance what will happen with the packages you have already installed here.
WINDOWS ->> Open CMD/Powershell as an administrator and type "R" to go into interactive mode. If this does not work, search and run RGui.exe instead of writing R in the console ...and then:
lib_path <- gsub( "/", "\\\\" , Sys.getenv("R_LIBS_USER"))
install.packages("installr", lib = lib_path)
install.packages("stringr", lib_path)
library(stringr, lib.loc = lib_path)
library(installr, lib.loc = lib_path)
installr::updateR()
MacOS ->> You can use updateR package. The package is not on CRAN, so you’ll need to run the following code in Rgui:
install.packages("devtools")
devtools::install_github("AndreaCirilloAC/updateR")
updateR(admin_password = "PASSWORD") # Where "PASSWORD" stands for your system password
Note that it is planned to merge updateR and installR in the near future to work for both Mac and Windows.
Linux ->> For the moment installr is NOT available for Linux/MacOS (see documentation for current version 0.20). As R is installed, you can follow these instructions (in Ubuntu, although the idea is the same in other distros: add the source, update and upgrade and install.)