Fossils of Rhamphinion were first discovered in 1978 when an expedition conducted by the Museum of Comparative Zoology at Harvard University and the Museum of Northern Arizona led by Farish A. Jenkins Jr. collected several small pterosaur fossils from the sandstone deposits of the Kayenta Formation, dating to the Early Jurassic (188 mya -185 mya) in Coconino County, northern Arizona, USA.

In 1981, James M. Clark of the University of Chicago collected a nearly complete fourth wing metacarpal of a pterosaur from the Kayenta Formation strata at the “Airhead West” locality nearby.

The species name jenkinsi is after the discoverer of the fossils, Farish Alston Jenkins Jr.[1] At the time, it was the oldest known pterosaur specimen from the Western Hemisphere[1] (now overtaken by Caelestiventus).

Kevin Padian did not assign it to any family or suborder within Pterosauria, in his original description, but did note that the jugal was unlike that of pterodactyloids, and so may have belonged to a "rhamphorhynchoid", i.e. a basal pterosaur.

[1] Peter Wellnhofer agreed that a "rhamphorhynchoid" identity was very likely,[4] but David Unwin was more hesitant to classify its fragmentary remains in The Pterosaurs: From Deep Time, noting it only as a "possibly valid species of uncertain relationships.