The Vanishing of Ethan Carter had Steam trading card support added on September 25, 2014. There are 6 cards in the series, and you'll receive 3 cards at random for purchasing and playing the game.
The Vanishing of Ethan Carter Redux also has Steam trading cards. When you purchase this game, you also receive the Redux version of the game, which will appear as a separate application in your Steam library. Running the Redux version of the game will give you cards from the The Vanishing of Ethan Carter Redux series, which the main application will give cards from this series.