His father, also named Rougned, played college baseball for the University of New Orleans. He has a sister and a younger brother, Rougned José Odor, who signed with the Texas Rangers organization on February 19, 2015. His uncle, Rouglas, played for eight seasons in Minor League Baseball for the Cleveland and Milwaukee Brewers organizations, and is now a manager with the Akron RubberDucks. Three of his uncles on his mother's side played baseball. All three played for the Aguilas de Zulia in the Venezuelan Professional Baseball League, while Eduardo Zambrano also played in MLB for the Chicago Cubs.
Odor began 2015 as the Rangers' starting second baseman, but he struggled mightily, hitting .144 with one home run, 9 RBIs, and 25 strikeouts to go with seven walks in 29 games. He was optioned to the Round Rock Express of the Class AAA Pacific Coast League on May 11. However, upon his demotion, Odor found his stroke, beating up Triple-A pitching to a .352/.426/.639 slash with five home runs, 19 RBIs, and only 10 strikeouts to 12 walks in roughly the same number of appearances. On June 15, following an injury to Delino DeShields Jr., Odor was recalled to the Rangers, and in his return, promptly went 3-3 with 2 RBI against the Dodgers. Rougned proceeded to hit very hot in the month of June, hitting .391 with two home runs and 9 RBIs and hit .319 with five home runs and 16 RBI in July.