The World of Warcraft Trading Card Game (WoW TCG) was discontinued in 2014, and its official digital client, the WoW TCG Arena, was shut down shortly after. There is currently no official online platform to play the game in its original form.
If you're looking for a supported online card game experience in the Warcraft universe or with similar strategic depth:
While the original WoW TCG lives on only through community efforts, these modern alternatives offer robust, officially supported digital card gaming experiences.