Rodriguez overcame a broken jaw to win a unanimous decision over Mexico’s Cristian Gonzalez in San Antonio, Texas, to become a two-weight world champion at the age of 23, BBC Sport reported.
After a dominant performance, judges scored the fight 118-110, 117-111, 116-112 for the American, who later revealed his jaw was broken in the sixth round.
Rodriguez had vacated his WBC super-flyweight title to move down a division.
And when asked what came next, he called out fellow Matchroom fighter and IBF flyweight champion Edwards.
“Sunny Edwards, that’s the only option. I think he’s been talking so let’s make it happen,” he said.
Undefeated Edwards, 27, had himself called out Rodriguez after retaining his title with a unanimous points win over Felix Alvarado in November.
Rodriguez is also unbeaten after 18 fights, winning 11 by knockout.