Martí formerly played for the Cuba national baseball team and Industriales of the Cuban National Series.
Martí was 1-0 with two saves and no earned runs at the 2006 World Baseball Classic, helping Cuba to a second-place finish. He was named to the all-tournament team. He also pitched for Cuba in the 2007 Baseball World Cup, coming one out short of a seven-inning perfect game against Venezuela.
Martí was originally slated to play in the 2009 World Baseball Classic, but he and Yasser Gómez were kicked off the team in November 2008 for an unspecified reason, believed to be an attempted defection to the United States. Marti, Gómez and Juan Yasser Serrano reportedly defected from Cuba in December 2008 in an effort to get to the Dominican Republic to seek a Major League Baseball career. In August 2009, they were declared free agents.
Martí pitched in the Dominican Winter Baseball League in the winter of 2009-10 and joined Veracruz of the Mexican League in 2010, going 2-2 with a 4.19 ERA in eight starts.
Martí signed with the Oakland Athletics as a free agent to a Minor League contract on August 6, 2010. Martí was invited to spring training with the Athletics in 2011 as a non-roster invitee. He played the 2011 season with the Stockton Ports of the Class-A Advanced California League, the Midland RockHounds of the Class-AA Texas League, and the Sacramento River Cats of the Class-AAA Pacific Coast League.