In a small bowl, whisk together the honey, soy sauce, ketchup, and minced garlic until smooth.
Spray the slow cooker insert with cooking spray to prevent sticking.
Place the chicken drumsticks in the bottom of the slow cooker, arranging in a single layer if possible (they may be stacked if needed).
Pour the prepared sauce evenly over the drumsticks, turning the pieces to coat if they are stacked.
Cook on high for 4 hours or on low for 6 hours, until the chicken reaches at least 160°F and is tender (170–175°F preferred).
Remove the drumsticks and serve warm.