Planets do not twinkle as stars do , beacuse the planets are not so far away from the earth as the stars are. So the light from the planets don't cover as many layers of atmosphere as the light from stars do. So the amount of refraction taking place is also less. Hence they don't appear to twinkle.
Moreover they do not have light of their own, they reflect the light of the sun and hence is not possible for them to twinkle when the light of the sun is not reflected by them.