Gaius Asinius Frugi (born c. 80), was a Roman moneyer who was officially permitted to mint money for use in Phrygia between 98 and 116. He was probably a descendant of Nicomachus (c. 30 BC - aft. 1 BC), a notable of Lydia in 1 BC.
He married and probably was the father of Gaius Asinius Rufus (c. 110 - after 136), who was also a notable in Lydia in 134 and 135 and became a Roman Senator in 136, and who married Julia, daughter of A. Julius Claudius Charax (c. 115 - after 147), granddaughter of G. Julius Lupus T. Vibius Varus Laevillus (c. 95 - after 132) and wife Julia Quadratilla and through her great-granddaughter of Gaius Julius Quadratus Bassus, suffect consul in 105, and wife Julia, Princess of Cilicia and had issue.