Can `sys.aud$` recycle itself?
The audit table does not 'clean' itself.  And there is not just a simple setting, like an init parameter, to do so.  You have to set up and schedule jobs to do that, and @eckes gave you a link to the documentation.  That same package (dbms_audit_mgmt) also provides a procedure for moving the audit table to another tablespace, getting it out of SYSTEM.  I strongly recommend you do so.  I just create a new tablespace dedicated to the audit table(s) and their indexes.