A rotary drill bit assembly suitable for directionally drilling a borehole into an underground formation, the drill bit assembly having a bit body extending along a central longitudinal bit-body axis, and having a bit-body face at its front end, wherein an annular portion of the bit-body face is provided with one or more chip-making elements; a pilot bit extending along a central longitudinal pilot-bit axis, the pilot bit being partly arranged within the bit body and projecting out of the central portion of the bit-body face, the pilot bit having a pilot-bit face provided with one or more chip-making elements at its front end; a joint means arranged to pivotably connect the pilot bit to the bit body so that the bit-body axis and the pilot-bit axis can form a variable diversion angle; and a steering means arranged to pivot the pilot bit in order to steer the direction of drilling.