The publishers of D&D have always been very careful about Religion and D&D.  It was clear from the start that real world religion inspired many of the things in the game, but they did try to keep things under wraps, or at least change the names.  The Cleric was originally modeled after the Knights Templar, who were forbidden to shed blood and thus had to use blunt weapons.  That's where the early restriction on weapons came from for that class.  There are still Druids in the real world.  The Paladin class was based on older legends that were then translated through the eyes of a major religion and became the Knights Of The Round Table.

The Monster Manual proved problematic.  Demons and Devils.  In particular, they took the names of many of the higher up demons and devils out of the records of a major religion and put stats to them.  This was considered naughty.  There was quite the fuss about the picture of the Succubus.  Naked!  Goodness gracious!  One of the major components of the Great Satanic Panic.  That's where we got "Bazetu and Tanari" from, and why we now have "Celestials" and "Fiends".  They continue to push the envelop though.  We have Angels now, and those used to be "Deva".

There have been similar problems with cultures.  There was once a setting called Al Quadim.  It was Arabian in flavor.  Nothing in it was really objectionable that I could see, but there are still people living in the lands known as Arabia.  The setting seems to have vanished.  We don't appear to have an Oriental Adventures yet either.  Voodoo in all it's many variations is pretty much the same deal.  It's not nice to make mock of things still practiced in the real world, unless it is clear from the start that you are joking, and even then, it's something to be handled with care.

I still think that Bard is the best fit.  No other class is as good at bedazzling a crowd, influencing them with methods both mundane and magical, and doing things to help or hinder actions.  Bards are great masters of illusion and charm type spells.  If they really have to, they can throw a Bane or another sort of curse, use magic for scrying, find out information with other spells, and even heal people.  Bards can raise the dead, and if that's really what you want, almost any character can take a feat and learn to animate the dead.  I'm not clear yet on what the Original Poster wants.  Any character can be a stereotypcial voodoo practitioner with a wooden mask and totem, chicken bones, frog eyes, and other stuff for weird rituals (bonus points for crazy chanting), voodoo dolls, spirits, and other cursing/hex magic, and also be known as witch doctors.  Some are better at it than others.  An Artificer - Alchemist can do pretty much any of it.

Quote from Lyxen >>

Honestly, it seems to me that the Loa would make wonderful patrons, and they would probably deserve a sub-class, and even with slight variations depending on the Loa, Baron Samedi probably would be different from Maitre Carrefour. :)

 
They sure would. But who knows where the story goes. Poor old babuschka Baba Yaga might get lost soon, considering we still have ve'dma all around in russia. Now i want chicken feet! Hungry! :D

Yeah, in terms of how OP's clarified their question, absolutely any class can work, since they're after an aesthetic, not anything to do with the actual religion they claimed they were trying to model.  Someone else correctly pointed out that you could make the same ask for Judaism - you can wear a yarmulke and a tallit without any specific class attached to you.  That means there are no design challenges presented - I originally thought they wanted to know how to actually be empowered by something that could be reasonably flavored as something akin to the Loa, so I answered accordingly, but they're literally after being a Disney villain.  I can do that with any class, it's not hard.  Not sure about any subclass, but probably.  Trying right now to think of a Barbarian subclass I couldn't reflavor and coming up empty.

Step 1: Identify a class/race/etc that seems like it would be fun to play.

Step 2: Take options within that class that seem to fit with your concept, or reflavor them to do so.

My voodoo character was a Phantom Rogue multiclassed with a Totem Barbarian. He could speak with spirits, infuse them into his body, and use them to attack. If you roleplay as a spooky shaman, that's 90% of it right there. The other 10% is describing your abilities to fit the mechanics you've chosen.

I've played an artificer/alchemist stylized as a witch (the European fairy tale style like). I've refluffed the spells as a potions/dusts that I threw around, so something similar might work for you.

Quote from Geann >>

Ok.  Bard.  College of Spirits.  Charlatan background.  They come from some exotic place your DM will have to set up for you, so they speak Common with an accent that makes them difficult to understand at times.  They wear fancy costumes to impress their audience.  99% of what they do is fakery, but they are highly entertaining, which is the stereotypical Voodooo Practitioner in most forms of entertainment I have seen.  If then need to, they can back up their stuff with real spells and bardic abilities.  The Spirits you can summon do helpful things after all.  If all else fails, cast Bard spells, such as Bestow Curse, or Comprehend Languages, or Clairvoyance.  Call yourself "Miss Cleo" for added effect.

 I like this idea and actually want to run with this character myself, but I'm going to start with Undying Warlock before going into Spirits Bard. The fakery is for the foot traffic. The real magic is for those who can pay the price.

Edit: Variant Human with the Chef feat

I just wanted to point out the distinction between Voodoo and Hoodoo. Hoodoo is the voodoo with the Cajun flair. While there are similarities between the two, I would highly recommend reading up a bit more before blindly appropriating cultural aesthetics you might know nothing about into a game. 

I am about to do this with a College of spirits bard. 

Taking debuff and damaging spells and some magic items that thematically fit.

I actually made a hombrew feat/spell a while ago for a friend, so I'll post it here (be aware it got abandoned years ago and left to marinate with a ton of older projects i did, so it most likely will not be balanced, and i don't post often cause i feel weird doing it)

Stichwork Curse

Prerequistes: The Ability to cast a 5th Level spell OR the ability to cast Curse

When you take the feat, you magically gain a featureless Doll. As a Bonus Action, you can cause the Doll gains the features of one creature you can see within 120 feet of you . The Doll has the same AC as the target, a Speed of 0 Ft (Any benefits of speed are ignored), and hitpoints equal to the original target. The Doll and the original target then become magically linked. Whenever you cast a spell or make an attack,  you can instead target the doll. Any benefits or effects dealt to the Doll are inflicted on the target. The Doll cannot be destoyed unless the cursed target dies or drops to 0 Hit points, in which case the doll becomes featureless once more. The Doll also becomes featureless one hour after it gains features. This trait/spell has a 50% chance to instead transform The Doll into the caster if used more than 3 times a day, in which case the Doll takes 1d10 Force damage every round. If the Doll is destroyed, a new one reforms the next dawn.

Edit: Wrong Version. That was when I was brainstorming T-T

College of Spirits Bard.  It was designed to be a voodoo type subclass.  You can find it in the Ravenloft source book.

My first thought was also college of the spirits bard.