Brazoban was second in the Mexican League last season with 9.99 strikeouts per nine innings. He previously pitched in parts of five major league seasons with the Los Angeles Dodgers, most recently in 2008. He was signed by the New York Mets in mid-August and pitched for Triple-A Buffalo.
Texas also agreed Thursday on a minor league deal with switch-hitting outfielder Hirotoshi Onaka, who hit .327 in 75 games the last four seasons at International Pacific University in Japan.
Japanese right-hander Yoshinori Tateyama agreed to a major league contract with Texas last month.