Iron fertilization of macronutrient-rich but biologically unproductive ocean waters has been proposed for sequestering anthropogenic carbon dioxide (CO2). The first carbon export measurements in the Southern Ocean (SO) during the recent SO-Iron Experiment (SOFeX) yielded ~900 t C exported per 1.26 t Fe added. This allows the first realistic, data-based feasibility assessment of large-scale iron fertilization and corresponding future atmospheric CO2 prognosis. Using various carbon cycle models, we find that if 20% of the world's surface ocean were fertilized 15 times per year until year 2100, it would reduce atmospheric CO2 by $lesssim$15 ppmv at an expected level of ~700 ppmv for business-as-usual scenarios. Thus, based on the SOFeX results and currently available technology, large--scale oceanic iron fertilization appears not a feasible strategy to sequester anthropogenic CO2.