Can a tattoo be removed by placing Apple cider vinegar on it for long periods of time?

No. Vinegar will not remove a tattoo. I do not recommend any other home remedies, especially abrasion methods.  You are just looking for trouble. Please seek professional treatment. The best way to remove a tattoo is with a PicoSure laser. Find one near you. Best of luck.

Laser tattoo removal is the gold standard for tattoo removal. Other options may cause permanent scarring if done incorrectly. Best, Dr .Karamanoukian Los Angeles

Tattoo ink is placed in the dermis and will not be exposed to the apple vinegar or any topical products. Lasers will penetrate the dermis and destroy the tattoo ink and that is how they work. 

The best option to permanently remove your
tattoo is the Picosure Laser. This laser will remove your tattoo in fewer
treatments than ordinary lasers while not causing harm to the surrounding
tissue. Consult with your doctor about the new Picosure Laser.