We present observations of the formation process of a small-scale filament on the quiet Sun during 5 - 6 February 2016 and investigate its formation cause. Initially, a small dipole emerged, and its associated arch filament system was found to reconnect with overlying coronal fields accompanied by numerous extreme ultraviolet bright points. When the bright points faded, many elongated dark threads formed and bridged the positive magnetic element of the dipole and the external negative network fields. Interestingly, an anticlockwise photospheric rotational motion (PRM) set in within the positive endpoint region of the newborn dark threads following the flux emergence and lasted for more than 10 hours. Under the drive of the PRM, these dispersive dark threads gradually aligned along the north-south direction and finally coalesced into an inverse S-shaped filament. Consistent with the dextral chirality of the filament, magnetic helicity calculations show that an amount of negative helicity was persistently injected from the rotational positive magnetic element and accumulated during the formation of the filament. These observations suggest that twisted emerging fields may lead to the formation of the filament via reconnection with pre-existing fields and release of its inner magnetic twist. The persistent PRM might trace a covert twist relaxation from below the photosphere to the low corona.