We describe a method for 3D object scanning by aligning depth scans that were taken from around an object with a Time-of-Flight (ToF) camera. These ToF cameras can measure depth scans at video rate. Due to comparably simple technology, they bear potential for economical production in big volumes. Our easy-to-use, cost-effective scanning solution, which is based on such a sensor, could make 3D scanning technology more accessible to everyday users. The algorithmic challenge we face is that the sensor's level of random noise is substantial and there is a nontrivial systematic bias. In this paper, we show the surprising result that 3D scans of reasonable quality can also be obtained with a sensor of such low data quality. Established filtering and scan alignment techniques from the literature fail to achieve this goal. In contrast, our algorithm is based on a new combination of a 3D superresolution method with a probabilistic scan alignment approach that explicitly takes into account the sensor's noise characteristics.