Yes, AWeber sign up forms fully support HTTPS/SSL submissions. If your site is HTTPS/SSL, publishing AWeber sign up forms to the site would not adversely effect the security of the site. If your website is not HTTPS/SSL, you can still publish AWeber sign up forms to your site without issues.
What If I Want To Use A Custom Form Rather Than An AWeber Sign Up Form?
If you wish to create your own sign up forms without the "Sign Up Form Generator", the forms' action must be set to:
<form method="post" action="https://www.aweber.com/scripts/addlead.pl">
Since AWeber Sign Up Forms Are Secure, Can I Collect Any Secure Information From My Subscribers?
While AWeber sign up forms do fully support HTTPS/SSL submissions, it is still a best practice to not utilize your sign up forms to collect sensitive information from your subscribers such as passwords, credit cards, or social security numbers.
Since you'll be using your AWeber sign up forms to collect subscribers on your mailing list, we would advise only collecting necessary information for your campaign. This information could be fields such as email address, name, birthday month, interests, etc.
For more information on email marketing best practices, click here!