Does the card gained from Stacked Deck count as drawing a card?

Based on the card text and related FAQs, no, the card gained from Stacked Deck does not count as drawing a card.

According to RiftJudge FAQ #6744, Stacked Deck specifically uses the phrasing "put into your hand" rather than "draw." In the rules of Riftbound, these are distinct mechanics. "Drawing" is defined in Rule 413.1 as a specific action of taking a card from your deck and adding it to your hand; because Stacked Deck instructs you to "put" the card into your hand, it does not trigger any effects that rely on "drawing" a card.