Saute kielbasa, onion and garlic in oil in large pot over medium-low heat until tender, about 10 minutes.
If using fresh kale, cut off stems and slice into 1/2-inch pieces. Keep stem pieces separate. Coarsely chop fresh leaves.
Add to the pot the chicken broth, 4 cups water, carrot, marjoram, salt, pepper and sliced fresh kale stems or frozen kale, if using. Bring to boiling. Lower heat; cover and cook for 15 minutes longer. If using fresh kale, add the leaves at this point along with the rice to the pot. Bring to boiling. Lower the heat; cover and simmer for 15 minutes or until the rice is tender.