I wanted to do something similar. I wanted to be able to click on an email icon and open a subscribe by email form. I’m using Feedburner.
I contacted the folks behind the Lightbox Pop plugin (XYZScripts). They said their premium version of the plugin would do this, if I want to buy it. Which, of course, makes me think of comparing the various for purchase popup plugins to find the best one and the best price … Too much work.
So, I got to thinking. The advantage of a popup is that the reader doesn’t have to navigate away from the page. They fill out everything in the popup then close it and they’re back on the page. Very handy for people viewing on a smartphone or pad/tablet. But this meant I would have to figure out how to open the subscription form and the feedburner page in the popup or popups. So, I went with something SIMPLER for now.
FYI, the Feedburner form opens a new window that looks like a popup. The Feedburner link opens a new window or tab. (I wonder if you could specify in the Feedburner link to open a small window like the form does so it also looks like a popup?)
I placed the link code supplied by Feedburner in a text widget (along with some other social media icons). I also set up styling for the social media icons in my child style.css. Here’s the code I used in the text widget.
<a href="https://feedburner.google.com/fb/a/mailverify?uri=YourFeedburnerCode&loc=en_US" class="social-icons-sidebar" title="Subscribe to YourBlog by Email" target="_blank"><img src="https://www.yourblog.com/wp-content/uploads/2012/11/email_48x48.png" /></a>
And here’s how it looks on my website.
Hope this helps. Be interested to know if you find a popup plugin that works.