After attending Brownsville Area High School,[1] he began his 19-season playing career in the Dodgers' organization in 1949, and was called to the majors in 1955 after winning 45 games over three years for the Triple-A Montreal Royals.

Roebuck made one appearance in the 1955 World Series against the New York Yankees, pitching two scoreless innings in Game 6 in relief of Russ Meyer in a 5–1 Brooklyn defeat.

His first two seasons as a Dodger in Los Angeles were ruined by a sore arm (1958),[6] then a year-long minor league demotion (1959) that cost Roebuck the chance to earn a second World Series ring.

Roebuck was able to return to form at Triple-A and spend the next six full seasons in the majors, although he again experienced arm trouble in 1961, worked in only five games, and spent part of the year on the Dodgers' voluntarily retired list.

In the decisive third game, officially the 165th regular season contest each team would play in 1962, Roebuck relieved Podres in the sixth inning and held the Giants scoreless for the next three frames, as the Dodgers took a 4–2 lead.

[7] His successor on the mound, Stan Williams, then allowed a sacrifice fly to tie the game and issued a bases-loaded walk to give the Giants the lead; an insurance run then scored on an error.

San Francisco won the 1962 National League pennant, with Roebuck charged with only his second loss in 12 decisions on the season, although his 64 appearances and ten victories were career bests.

[8] In 1964, still an active player with the rival Phillies, Roebuck was asked by Roy Hofheinz, owner of the Houston Colt .45s, to hit the highest fungo fly balls he could in order to determine the ideal roof height for baseball's first domed stadium, the Astrodome, still under construction at the time.