There are those who believe that there is an actual process through which people can be transformed into zombies. The purported process involves traditional practices and the use of psychoactive drugs. An ethnobotanist named Wade Davis investigated claims of actual zombies in Haiti, and in the1980s published two books: The Serpent and the Rainbow and Passage of Darkness: The Ethnobiology of the Haitian Zombie. In these books Davis claimed that a combination of powders could keep people in a zombie-like state. Those powders included drugs such as datura and tetrodotoxin. According to Davis, in combination with acceptance and conformation with Haitian tradition and culture, these drugs contributed to people believing they were zombies and acting accordingly.
There are some problems with these claims, and they are widely discounted in the scientific community. For one, tetrodotoxin is a powerful paralytic found in pufferfish. Part of the delicate art of preparing pufferfish as a meal is avoiding the possibility of killing the consumer due to paralysis. While tetrodotoxin can certainly change the living to the dead, tetrodotoxin alone is not sufficient to create the living dead.
That said, a combination of different psychoactive medications can certainly reduce someone's level of consciousness and make them more susceptible to suggestion. That's the principle behind sedating medications used for dangerously incoherent hospital patients, and more insidiously for so-called "truth serums." Truly believing that a certain outcome will result from anything, whether a medication or ritual, can also have powerful physiological effects. This is the reason why well-designed clinical trials must include an inert placebo as well as actual medications. If someone believes they are getting an actual drug to treat their disease, they will often have improvement of some of their symptoms even if all they're actually ingesting is sugar.
There are limits to the power of suggestion, though. Is it possible that a combination of drugs and belief in strong cultural traditions could result in someone behaving like a zombie? Yes. But suggestion alone is unlikely to raise an army of the undead.