Are you having trouble installing R packages from the RStudio Server interface, @Sinval? Can you just open up RStudio Server and then install.packages() yourself?
Oops, I didn't read. If it's Linux packages, you could take a look at whether your department uses a module system and see whether some of the common ones needed (ncdf4 is a pretty important one for me, for example, but I imagine a C or CPP compiler would be on your list) can just be loaded in without admin help.