Yes, the USN's ASW Mk 24 'mine', but no air dropped antishipping homing torpedoes, AFAIK.
The "Fido" or MK 24 "Mine" was in all senses a homing torpedo but I suspect it got called a "mine" because it didn't run a set depth or because of security attempting to keep its existence a secret.
The Germans also used acoustic homing torpedo's the G7es series which came in a versions to home on to merchant ships and escorts (which were likely cavitating). More advanced versions that would do a dog leg around a seductive noise source such as foxer came in to service near the end of the war and there was a wire guided version called spinne (spider). The Germans never air dropped these though.
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