A pipe torquing sprag tool comprises one or more elastomeric sprags supported on a sprag support in an arrangement lying generally in a plane that is generally perpendicular to the axis of the rotatable sprag support. Each sprag has a solid, uninterrupted side and an interrupted side, and each sprag reacts to a lateral force in the general direction tangential to the surface of the sprag support and applied near the top of the sprag to bend the elastomeric sprag either toward the interrupted side to at least partially lean, fold or collapse, or towards the substantially uninterrupted side for being deformed to a generally compressed and non-compliant configuration for gripping. The sprag tool of the present invention may comprise a sprag support for positioning an external arrangement of sprags for being inserted into the bore of an add-on pipe segment. Alternately, the sprag tool of the present invention may comprise a sprag support for positioning an internal arrangement of sprags for being received over the end of an add-on pipe segment.