CiviCRM Community Forums (archive)

You can set the membership period as 1 month for a given membership type AND you can send reminders with a link to members to renew each month automatically (using the Update Membership script and a cron job):

http://wiki.civicrm.org/confluence/display/CRMDOC/Membership+Types (see the 2nd half of the page on membershp renewal reminders).

However, there is no support as of yet for automatically billing membership renewals - which I suspect is what you're looking for. There is some discussion among some community members about sponsoring / contributing improvements in "recurring payment" support - which could be tied in to this. If you have engineering resources - you might consider helping with this.