Martinez graduated from Belen Jesuit Preparatory School in Miami, Florida, and enrolled at Fordham University. He is the 34th Fordham alumnus to make it to the Major League Baseball (MLB). He was 1-3 with a 5.33 ERA in 15 games, over 2 seasons for Fordham as a relief pitcher. But he was mostly a second basemen, batting .295 with 4 HR, 66 RBI, 167 hits, and 22 stolen bases over 3 seasons and 148 games. Martinez also played in a collegiate summer baseball league, the New England Collegiate Baseball League, for the Vermont Mountaineers. He is the seventh Mountaineer to make it to the MLB.
Martinez was named the Rangers' fifth starter on March 26, 2014. In his first career start against the Tampa Bay Rays, Martinez went six innings, struck out three and allowed three earned runs on four hits. He received a no decision as the Rangers lost 5-4. After two straight starts against the Oakland Athletics, the Rangers got Matt Harrison back from the DL and moved Martinez to the bullpen. Martinez went 6.2 innings, struck out six and allowed only one earned run in four relief appearances. In a game against the Houston Astros, Harrison injured his lower back and had spinal fusion surgery. The Rangers then put Martinez back into the starting rotation.