Can I use Arcane Shift on my unit that's being targeted by a unit to avoid being targeted?

No, you cannot use Arcane Shift to save your unit from being targeted by an opponent's spell or ability that is already on the chain.

According to RiftJudge FAQ #9372, Arcane Shift is an [Action] speed spell. Action spells can only be played during an OPEN state (when no chain exists). Once your opponent plays a spell or ability targeting your unit, that item is placed on the chain, and the game state immediately becomes CLOSED. Because the state is now closed, you cannot play an Action speed spell like Arcane Shift in response.

Why this interaction works this way:

1. State Requirements: Per Rule 309.1, if a chain exists, the turn is in a CLOSED state. Per Rule 309.1.a, only cards and abilities with the [Reaction] keyword can be played or activated in a closed state.
2. Action vs. Reaction: Arcane Shift has the [Action] keyword (as seen on the card and confirmed by Rule 158.2.a). It does not have the [Reaction] keyword. Therefore, it is restricted to being played only when the chain is empty (an open state).
3. Targeting: Even if you were in an open state, Arcane Shift requires you to target both a friendly unit and an enemy unit at a battlefield to be played (as confirmed by RiftJudge FAQ #378). You cannot play it solely to "blink" your unit if there is no valid enemy unit to target for the damage portion of the spell.

In summary, because Arcane Shift is an Action speed spell, it cannot be used to respond to an opponent's action that has already created a closed state. You would need a card with the [Reaction] keyword to respond to an effect already on the chain.