If you have access by SSH to the server, then you can:
1) Gzip the old file (text files compression ratios are really good). If we assume the file is named /var/log/apache/access.log then do this:
gzip -c /var/log/apache/access.log > /var/log/apache/access.log.gz
2) Clear the current file
echo > /var/log/apache/access.log
3) Restart apache