Rdio's login, payment, and signup forms are served in iframes-over-SSL to ensure the security of your personal information. Your browser will not show the HTTPS indicator unless you open the form in a popup window.
Before logging in, adding new subscription information on the Subscription page, or while adding or editing details in the payment information pop-up, click the "More info" link to access the HTTPS popup:
Then click, "open this form in a new window"
From there, enter your information in the popup window, which is served through HTTPS: