An attachment system (10) for a turbine airfoil (12) including one or more roots (14) to attach the turbine airfoil (12) to a rotor, whereby the roots (14) have one or more curved teeth (18) that substantially limit, if not completely eliminate, circumferential rocking motion of the turbine airfoil (12) relative to a disc (20) supporting the turbine airfoil (12) during turning gear operation. The curved configuration of the teeth (18) extending laterally from the root (14) prevent rotation of the turbine airfoil (12) relative to the disc (20) supporting the turbine airfoil (12), thereby preventing premature failure of the turbine airfoil (12) or disc (20) due to wear from turbine airfoil (12) rocking during turning gear operation. In at least one embodiment, a laterally extending outer edge (22) of an axially extending tooth (18) may be curved about an axis (30) orthogonal to a centerline (26) of a turbine engine (28) in which the turbine airfoil (12) is positioned.