The present invention provides: a novel production technique that enables production of a polymer whose molecular weight and molecular weight distribution are controlled and production of a polymer having a complicated structure in a desirably controlled manner using commercially available materials without using a radical polymerization initiator or a special material for use in living radical polymerization and without the need for strict polymerization conditions; and a radical polymerization initiating group-containing compound for use in the technique. The present invention relates to: a method for producing a polymer, the method including a polymerization step of mixing and warming (1) a radically polymerizable monomer, (2) an organic compound wherein at least one group that functions as a group for initiating polymerization of the monomer and that has a structure represented by formula 1 or formula 2 (X in the formula represents Cl or Br) is introduced in a molecule of the organic compound, and (3) an iodine-containing compound, thereby initiating, from the group having the structure, radical polymerization accompanied by a termination reaction; and the organic compound of (2) for use in the method.