As can be seen in this link, this is a very complicated question. A full answer would have to take into account things like the different life spans of people in different income groups and would have to compare what people in various groups paid in to Social Security and got out of it.
The average Social Security recipient pays less money into the system than he or she takes out. In that sense, it can help to redistribute income. But there is also a cap on earnings above which Social Security taxes are not taken. This limits the degree to which any redistribution can happen.
The study in the link above concludes that Social Security has a very small impact in terms of increasing income equality.