Leptellina rhacta was named by Williams (1962). Its type specimen is BB.26031, a shell (complete shell), and it is a 3D body fossil. Its type locality is South-east side of quarry, ½ mile north-east of Brockloch Farm, which is in a Llandeilo carbonate mudstone/limestone in the Stinchar Formation of the United Kingdom.

It was recombined as Leptellina (Leptellina) rhacta by Candela and Harper (2014).