Historical Rules · 15 February 2021
Rule 702.64b
Official source text from the 15 February 2021 Rules release
If either half of the exchange can’t be completed, the ability has no effect. Example: You activate the aura swap ability of an Aura. The only Aura card in your hand can’t enchant the permanent that’s enchanted by the Aura with aura swap. The ability has no effect. Example: You activate the aura swap ability of an Aura that you control but you don’t own. The ability has no effect.