Edit the file below:
nano /etc/rsyslog.d/50-default.conf
Comment the line below:
#*.*;auth,authpriv.none -/var/log/syslog
Add the following lines (limit to 2 GB in the example and remove the file when it reaches the limit)
$outchannel mysyslog,/var/log/syslog,2147483648,/bin/rm /var/log/syslog
*.*;auth,authpriv.none :omfile:$mysyslog
Restart rsyslog
service:
systemctl restart rsyslog.service