Thank you for your query and we are so sorry about the trouble this must have caused.
Can you please try this on an incognito window or private window to check if there’s still no action? A new tab should be opened whenever you try to connect your account to your website.
Also, please make sure that you are logged in to your Rank Math account first before doing the steps above.
Assuming you are using the latest version of all the plugins and the themes (please update if not yet), it would seem like a conflict with one of the plugins or the theme you are using.
Only the site admin would know and your users won’t be affected by this troubleshooting.
If the issue persists, please edit the first post on this ticket and include your WordPress & FTP logins in the designated Sensitive Data section.
Please do take a complete backup of your website before sharing the information with us.
It is completely secure and only our support staff has access to that section. If you want, you can use the below plugin to generate a temporary login URL to your website and share that with us instead: https://wordpress.org/plugins/temporary-login-without-password/