not through any additional packages

You can install modules even if you're not an administrator / root, see for example local::lib. (Sometimes, there are legitimate reasons for not being able to use a module, but those are rare!) You really should try to install modules that will help you, such as Statistics::R from AppleFritter's answer.

Running external commands is easier via helper modules, my two go-to modules are IPC::System::Simple as a drop-in replacement for system or IPC::Run3 for manipulating STDIN, STDOUT and STDERR.

Having said that, how to use system is explained in its documentation. In your case it would look something like this (untested):

system("R", "CMD", "BATCH", $R_FILENAME) == 0
    or die "calling R failed: $?";
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