Heat a large skillet over medium heat. Once hot, add the ground chicken and cook until browned, stirring occasionally, about 5-7 minutes.
Add the diced onion, bell pepper, and minced garlic to the skillet. Cook for an additional 3-4 minutes until the vegetables are softened.
Sprinkle the Cajun seasoning over the chicken mixture, and stir well to combine.
Pour in the tomato sauce, Worcestershire sauce, brown sugar, and apple cider vinegar. Stir and let simmer for 10 minutes, allowing the flavors to meld together. Season with salt and pepper to taste.
While the mixture simmers, lightly toast the hamburger buns in a separate skillet or toaster if desired.
Once the mixture has thickened up and is heated through, spoon it generously over the bottom halves of the toasted buns. Top with your choice of pickles, shredded cheese, or hot sauce.
Place the top halves of the buns on each Sloppy Joe and serve immediately.