Bring 2½ cups water to a simmer in a saucepan. Stir in the rice; cover and cook at a gentle, steady simmer until the water is absorbed, about 35 minutes.
Slice the sausage links ¼ inch thick. Heat just enough of the oil to lightly coat the bottom of a large, nonstick skillet. Cook the sliced sausages ver medium-high heat, gently turning them until all sides are golden brown. Remove from the heat and set aside until needed.
Heat the remaining oil in the same skillet. Add the onion and sauté over medium heat until translucent. Add the garlic, celery, and bell pepper, and continue to sauté until all the vegetables are lightly browned.
Add the remaining ingredients except the salt. Bring to a simmer, then cover and simmer gently for 15 to 20 minutes.
Combine the skillet mixture with the hot cooked rice and sausage pieces in a large serving bowl and toss together thoroughly.
Season to taste with salt (and a bit more cayenne if you’d like a spicier dish) and serve at once.