Patrick Sheridan was arrested in January 2015 in Holyhead, north Wales, on an indictment returned in May 2014 by a federal grand jury in Waco.
He and a co-defendant were accused of conspiring to traffic the horns of the critically endangered black rhinoceros.
Co-defendant Michael Slattery Jr pleaded guilty in New York to his role.
He was sentenced to 14 months in prison.
An Irish national has been sentenced to a year in prison after pleading guilty in Texas to trafficking rhinoceros horns.