The device, such as an autonomous cardiac implant of the leadless capsule type, has a device body with a means for its anchoring to a patient's organ wall. The anchoring means includes a screw with a helix wire wound into a plurality of non-contiguous turns, the screw having a clamped end integral with the front face of the device body and a free end with a beveled end defined by at least one oblique surface. The normal to the oblique surface of the beveled end is directed away from the front face, in such a way that the oblique surface is directed towards the patient's organ wall. The normal to the oblique surface forms an angle between 30° and 60° with respect to the helix axis, and the screw is elastically deformable in axial compression, with a stiffness coefficient of at most 5 N/mm.