Cut sausage into 1/4-inch-thick slices and chop onion, bell pepper, and celery. In a dry 2 to 2 1/2-quart heavy saucepan brown sausage over moderately high heat, stirring frequently, and with a slotted spoon transfer to paper towels to drain. Pour off any fat from pan and in pan cook vegetables in oil over moderate heat, stirring occasionally, until onion is softened. Stir in rice, broth, and cayenne and bring to a boil. Cover pan and cook rice over low heat 15 minutes.
Remove pan from heat and let rice stand, covered, 5 minutes. Thinly slice scallions. Fluff rice with a fork and stir in sausage, scallions, and salt and pepper, to taste.