Take a look at what the system comes with. From a quick check, I'm almost certain both CentOS and Fedora ship with rsyslog, which would lead me to believe that the Pi would have that or something very similar. If not, rsyslog does at least have an ARM package.
Pi runs Debian.
Yeah, I don't have any debian-based systems I can check right now, but I know it still has the mechanism built-in. Just might not be rsyslog.