Answer by Romeo Ninov for How to prevent rsyslog from logging cron tasks to /var/log/syslog using additional config

Line in you config:

*.*;cron,auth,authpriv.none     -/var/log/syslog

make it like this:

*.*;cron.none,auth,authpriv.none     -/var/log/syslog

to stop cron from logging in syslog

And also you can add dash (-) in front of the path for cron log to avoid flush of buffers on every write. So your cron line to become:

cron.*                          -/var/log/cron.log