A vertebral anchoring device includes connectors (2) linked to one another by connecting rods (3) and fixed on bone-anchoring screws (5) implanted in the vertebrae (4) of a vertebral column, each connector (2) being composed of a connection element (6) that includes receiving and fixing members to permit immobilization of the connecting rod (3) in translation and in rotation. Each connection element (6) includes, opposite the members for receiving and fixing the connecting rod (3), a seat (12) that cooperates with a connecting device (17) permitting assembly of the anchoring screw (5). The connecting device (17), before immobilization of the connecting rod (3) in the connection element (6), permits lateral and independent tilting movements of the connection element (6) and of the anchoring screw (5) relative to each other, and rotation of the anchoring screw (5) for fixing it in the body of the vertebra (4).