Do I need to have a friendly unit on the board in order to play Arcane Shift?

Yes, you must have a friendly unit on the board in order to play Arcane Shift.

According to RiftJudge FAQ #378 and FAQ #9022, Arcane Shift requires valid targets for both parts of its effect—a friendly unit to banish (and subsequently replay) AND an enemy unit at a battlefield to deal 3 damage to—in order to be played on the chain. You cannot play the spell if there is no enemy unit present at a battlefield, nor can you play it if there is no friendly unit to target for the banishment portion of the effect.