The present invention provides a rubber composition for a sidewall excellent in appearance and weather resistance, and a tire having a sidewall prepared by using the rubber composition. The rubber composition for a sidewall of the present invention comprises 45 to 60 parts by weight of a carbon black, not more than 1.5 parts by weight of powder sulfur, not more than 0.75 part by weight of a sulfenamide vulcanization accelerator and 0.7 to 1.5 parts by weight of paraffin wax in which the distribution of the number of carbon atoms is 20 to 50, the ratio (iso content/normal content) of iso content to normal content is 5/95 to 20/80, the standard deviation/average number of carbon atoms of the iso content is 1.0 to 1.8 and the standard deviation/average number of carbon atoms of the normal content is 1.0 to 1.8, based on 100 parts by weight of a rubber component comprising a butadiene rubber in an amount of 35 to 55% by weight and a natural rubber.