No, Dark Souls is not an Action/RPG.
Yes it is. Why wouldn't it be?
You play a character, character has statistics, statistics affect how you play. You can upgrade your gear, change your gear, gear affects play. It has other characters you interact with. It has hack & slash combat, that is affected by said stats and gear.
~WikipediaAction role-playing games (abbreviated action RPG, action/RPG, or ARPG) form a loosely defined subgenre of role-playing video games that incorporate elements of action or action-adventure games, emphasizing real-time action where the player has direct control over characters, instead of turn-based or menu-based combat. These games often use combat systems similar to hack and slash or shooter games.
It does fit into this subgenre. Yes, it is loosely defined, but it has all the characteristics of what I would call and action-RPG.