Combine popcorn and cranberries in a large mixing bowl, and set aside.
Combine sugar, 3/4 cup water, corn syrup, salt, and vinegar in a small, heavy saucepan. Set the saucepan over high heat, and bring the mixture to a boil. Insert a candy thermometer, and cook until the mixture reaches 290 degrees, about 14 minutes. Add food coloring, stirring, until desired color is reached. Remove pan from heat.
Pour the hot syrup over the reserved popcorn mixture; stir together with a wooden spoon until all the kernels have been well coated. Working quickly, use your hands to form a 2 1/2-inch-diameter ball. Transfer the ball to parchment paper, and let cool completely. Repeat with remaining the popcorn mixture. Store the popcorn balls in an airtight container up to 2 days.