As per the Blizzard's official Hearthstone Tournament Player Handbook v2.6 (from the official Hearthstone Website's eSports Rules and Policies), section 5.10 "Written Notes and Deck Tracking Software" permits deck trackers for tournament usage as long as tracker complies with the terms outlined in the player handbook and the tournament does not forbid deck trackers.

We believe that the Hearthstone Deck Tracker, as the most prominent and widely-used deck tracker for Hearthstone, fully complies with these rules. Our deck tracker enhances all levels of competitive play by allowing players to review their matches after the game and replaces the task of manually creating notes for each match.

If you're unsure about whether you may use Hearthstone Deck Tracker in a specific tournament, please reach out to your tournament organizers.