You can renew online using a credit card. Start HERE (at the AAUW site) and select Member Services Database (MSD) and log in. There’s a member lookup if you’re not sure of your AAUW membership ID. Once you’re logged in, select the Membership Payment Plan (MPP) or Personal Membership MPP to arrive at the payment form. The MPP will indicate when your membership expires and when you last paid.
You may also renew via mail, using this Branch form.