Depending on the version of Pega, you could configure prlogging.xml so that x number of log files are generated, with each log filling up until a size limit is reached. After the specified number of logs has been reached the oldest logs are overwritten. If you're interested in this, I can find the details (which will depend on the version of Pega in use).
Beyond that, I don't believe there is anything ootb that does this.
Unfortunately overriding the log file won't serve the purpose here because our requirement is to delete pega log files after certain period of time as it contain some customer related data. But thanks again for providing an alternative solution.