As of MySQL 5.1.12, you can rename the general query log file at runtime by disabling the log:
SET GLOBAL general_log = ‘OFF’;
With the log disabled, rename the log file externally; for example, from the command line. Then enable the log again:
SET GLOBAL general_log = ‘ON’;
This method works on any platform and does not require a server restart.
http://dev.mysql.com/doc/refman/5.1/en/query-log.html