Manipulation of small-scale matter is a fundamental topic in micro- and nanorobotics. Numerous magnetic robotic systems have been developed for the manipulation of microparticles in an ambient environment, liquid as well as on the air-liquid interface. These systems move intrinsically magnetic or magnetically tagged objects by inducing a magnetic torque or force. However, most of the materials found in nature are non-magnetic. Here, we report a ferrofluidic manipulator for automatic two-dimensional manipulation of non-magnetic objects floating on top of a ferrofluid. The manipulation system employs eight centimeter-scale solenoids, which can move non-magnetic particles by deforming the air-ferrofluid interface. Using linear programming, we can control the motion of the non-magnetic particles with a predefined trajectory of a line, square, and circle with a precision of 25.119.5 m, 34.428.4 m and 33.426.6 m, respectively. The ferrofluidic manipulator is versatile with the materials and the shapes of the objects under manipulation. We have successfully manipulated particles made of polyethylene, polystyrene, a silicon chip, and poppy and sesame seeds. This work shows a promising venue for the manipulation of living and non-living matter at the air-liquid interface.