Social scientists usually point out that the tax system is a fairly clunky way to do much income redistribution. It is too easy for a tax system to end up full of carefully crafted loopholes, after all, and wealthy individuals and corporations have plenty of cash lying around to hire good accountants to exploit them. If we add to that that taxes often have odd side effects and loss of efficiency, it is easy to understand why most countries do most of the redistribution on the spending side of fiscal policy, not the revenue side. Not surprisingly, most European countries pay for their welfare states using a fairly regressive value added tax.
A tax system, however, can do quite a bit of redistribution, depending on how it is designed. Some observers will call that social engineering or some other nasty word. Newt Gingrich, however, calls it his tax plan:
There is a nice amount of redistribution going on in that graph, but I am not sure if we can call it fair. The numbers are from the Tax Policy Center, via Money Box, and they are worth a good read. It also increases the deficit by more than a trillion, by the way. Just in case you were wondering.