Games like Arcana
Games like Arcana include Monster Train, Slay the Spire, Slay the Spire 2, Balatro, and 9 Kings. We matched them by the tags players give Arcana on Steam (Poker, Roguelike, Trading Card Game, Card Battler, and Turn-Based Tactics): closest matches first, and among equally close ones the better-known games.

Monster Train
Shared: Card Battler · Roguelike · Roguelite

Slay the Spire
Shared: Roguelike · Card Battler · Roguelike Deckbuilder

Slay the Spire 2
Shared: Roguelike · Roguelike Deckbuilder · Card Battler

Balatro
Shared: Roguelike · Roguelike Deckbuilder · Card Game

9 Kings
Shared: Roguelike · Roguelike Deckbuilder · Card Battler

Wildfrost
Shared: Card Battler · Roguelike Deckbuilder · Turn-Based Tactics

LONESTAR
Shared: Roguelike · Card Battler · Turn-Based Tactics

Trials of Fire
Shared: Card Battler · Turn-Based Tactics · Roguelite

Dream of Corpse Lady
Shared: Card Battler · Turn-Based Tactics · Roguelike

Dicey Dungeons
Shared: Card Battler · Roguelike · Roguelike Deckbuilder

As We Descend
Shared: Roguelike · Card Battler · Roguelike Deckbuilder

Inscryption
Shared: Card Battler · Roguelike · Card Game

Monster Train 2
Shared: Roguelike · Roguelike Deckbuilder · Turn-Based Tactics

Alina of the Arena
Shared: Roguelike · Roguelike Deckbuilder · Turn-Based Tactics

StarVaders
Shared: Roguelike Deckbuilder · Turn-Based Tactics · Roguelite

Touhou: Lost Branch of Legend
Shared: Roguelike · Roguelike Deckbuilder · Card Battler

Dungeons & Degenerate Gamblers
Shared: Roguelike · Roguelike Deckbuilder · Card Battler

Across the Obelisk
Shared: Roguelike · Roguelike Deckbuilder · Card Battler

Die in the Dungeon
Shared: Roguelike · Roguelike Deckbuilder · Card Battler

Astrea: Six-Sided Oracles
Shared: Card Battler · Roguelike · Roguelike Deckbuilder

Darkest Dungeon® II
Shared: Turn-Based Tactics · Roguelike · Roguelite

Roguebook
Shared: Roguelike · Roguelite · Card Game

He is Coming
Shared: Roguelike · Roguelite · Roguelike Deckbuilder

Griftlands
Shared: Card Battler · Roguelite · Roguelike