This is a landing page, or a landing page pop-up.
Yes, there are plugins that will do this for you. Try searching the plugin repository for them.
And yes, as much as you may like this, most readers don't. Anything that alienates readers by putting distance between them and your content will lower the number of people who come back to your website.
Personally, I just close the tab when a website does this. It's annoying and rude.