Logrotate

/etc/logrotate.d/syslog

/var/log/syslog
{
  rotate 7
  daily
  missingok
  notifempty
  delaycompress
  compress
  size 100k
  postrotate
                invoke-rc.d rsyslog rotate > /dev/null
  endscript
}

logrotate -d -f syslog