Here comes the bummer
The short answer to your question is: no. I made my living reviewing movies for years at places like the Village Voice, the NY Sun, Variety and a bunch of other publications. And this work just doesn't exist anymore.
If you live in a smaller market, try finding the smallest paper you can, send them a link to your blog where you've (hopefully) been writing reviews for a long time, and pitch them a review of something that's hasn't opened yet. Keep doing it and eventually they might assign something to you and congrats - you're on the bottom rung!
But in big markets - NY, LA, San Francisco, Chicago - you're out of luck. So many reviewers lost their jobs that editors have a backlist of dozens of people they can assign an article to before they try someone they don't know. And in general they'll assign it to someone on staff or a perma-lancer first.
However, don't despair, nepotism works! If you've got a buddy who's an editor, buy him or her lots of drinks and always pay for the bar bill and keep pitching funny takes on upcoming films. Eventually they'll either break down and assign you something or they'll be so drunk you can lift their wallet.