Arcane Shift

Yes, as long as the unit is not a token and you control that battlefield. For a non-token unit, by the time battlefield control is checked, the unit's owner has started playing it, leaving the unit pending on the chain while Arcane Shift finishes resolving.^{321.1354.2354.3} That pending unit keeps the chain active, so you keep control of the battlefield and may choose it for the unit's return.^{323.5330331.1355.2.a}

A token unit instead ceases to exist immediately after moving to banishment, before Arcane Shift can instruct its owner to play it again.^186.1

Steps

1. Arcane Shift banishes the unit, causing a cleanup.^319.6 Arcane Shift then instructs the unit's owner to play it, moving the unit to the chain as a pending item before the spell finishes resolving.^{354.2354.3420.3}

2. Cleanup runs while the unit remains pending, so the active chain prevents you from losing control of the empty battlefield.^{321.1323.5330331.1354.4}

3. During finalization, you choose the still-controlled battlefield as the unit's location.^355.2.a The unit then enters there.^359.2.c