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