ArcGIS supports raster data that is 12 bit held in a 2 byte (16 bit) container. However, if a raster only has 12 bits per pixel, then it is currently not supported.
For example, Space Imaging and Digital Globe create 11 bit rasters that are held in a 16 bit container. This means that out of 65,536 values possible, only 2,048 are utilized.
Space Imaging, such as IKONOS and Digital Globe images are supported by ArcGIS as these are both 11-bit datasets.