Fe3O4 nanoparticles in the size range of 8-12 nm have been prepared and allowed to self-assemble on GaAs substrates in the presence of strong magnetic fields. A long range ordering is observed in which the particles self-assemble into a distribution of elongated clusters with a predominant orientation lengthwise along the field direction. Hysteresis loops measured parallel and perpendicular to the alignment direction show substantial directional dependence. The coercive fields in the direction parallel to the alignment field are larger than those perpendicular to it by 57% and 136% at 100 and 5K, respectively. A broad peak is observed in magnetization profiles obtained with zero- field-cooling.