Providing Choice for Social Security Retirees Act This bill amends title II (Old Age, Survivors, and Disability Insurance) (OASDI) of the Social Security Act to allow an individual who is entitled to OASDI benefits to claim a delayed-retirement credit in a partial lump sum. Under current law, an individual's OASDI benefits are increased by a two-thirds of 1% for each month in which the individual, after attaining full retirement age but prior to attaining age 70, delays claiming those benefits. The bill allows an individual who delays claiming OASDI benefits to instead opt to receive a smaller percentage increase (one-half of 1%) for each applicable month, plus a one-time lump sum payable at the time of the individual's entitlement to the benefits. The amount of this lump sum shall equal the sum of the present values of one-sixth of 1% of the amount of the individual's monthly benefits for each month in the individual's life-expectancy period.