If you have a centralized syslog server, or you use Splunk for log tracking, you may find the need to get older log files into a syslog port on that server.
Edit: Using logger (as suggested by David and Jerry below) will give you a more reliable way to send the data to a syslog server:
cat some.log | logger -t UsefulLabel -h yoursyslogserver.com -p 514
You'll also be able to set a label for the text before it's piped into the syslog server, which would be handy if you're sorting or parsing the data later on.
Also, you can send your data in the raw using netcat:
cat some.log | nc -w 1 -u yoursyslogserver.com 514

Do it better with logger:
cat some.log | logger -t UsefulLabel
...will enter the contents of some.log, with UsefulLabel prepended to it.
...your syslog IS set up to log to a central location, right?...
David is correct. You will have much better luck using logger. I would add, though, that you can bypass the local syslog using logger:
cat some.log | logger -t UsefulLabel -h yoursyslogserver.com -p 514
Otherwise, you will have to have have your local syslogd set up to forward the messages on to yoursyslogserver.com, which may or may not be acceptable.