If you are able to use the bash shell, you can consider simply running the R code from within a bash script and piping the stdout and stderr streams to a file. Here is an example using a heredoc:
File: test.sh
#!/bin/bash
# this is a bash script
echo "Hello World, this is bash"
test1=$(echo "This is a test")
echo "Here is some R code:"
Rscript --slave --no-save --no-restore - "$test1" <<EOF
## R code
cat("\nHello World, this is R\n")
args <- commandArgs(TRUE)
bash_message<-args[1]
cat("\nThis is a message from bash:\n")
cat("\n",paste0(bash_message),"\n")
EOF
# end of script
Then when you run the script with both stderr and stdout piped to a log file:
$ chmod +x test.sh
$ ./test.sh
$ ./test.sh &>test.log
$ cat test.log
Hello World, this is bash
Here is some R code:
Hello World, this is R
This is a message from bash:
This is a test
Other things to look at for this would be to try simply pipping the stdout and stderr right from the R heredoc into a log file; I haven't tried this yet but it will probably work too.