Rosenbaum began playing football at the age of 13 for the Gadna Yehudayouth team. Two years later, he joined Hapoel Tel Aviv's youth team, which won the league championship in 1951. In 1951, he was promoted to the senior team of the club. He scored his first goal for the team against Maccabi Rishon LeZion on. During his time at Hapoel Tel Aviv, the club won their first championship since the Israeli war of independence, in 1957. In the 1957 season, Rosenbaum scored 9 goals, including two in a derby against Maccabi Tel Aviv, which was won 4-2 by Hapoel. In 1961, he was part of the team that won the Israel State Cup, beating then-champions Hapoel Petah Tikva in the final. On, Rosenbaum served as the team captain in a match against Shimshon Tel Aviv. The match was the first match ever played in the Bloomfield Stadium. He also served as captain in the official inaugural match of the studio on, against Dutch side FC Twente. Rosenbaum retired from playing football in 1965, having scored 78 league goals during his tenure, the fourth greatest amount of league goals ever scored by a Hapoel Tel Aviv player.
Rosenbaum was appointed coach of the Hapoel Tel Aviv youth team in 1965, and subsequently led it to the youth championship, with the young football player Ronnie Calderon starring the team under his coaching. After two years in the youth team, Rosenbaum was appointed head coach of Hapoel Tel Aviv. In his first season as head coach of the senior team, he led the senior team to the championship as well, with Calderon, Shiye Feigenbaum, Yehezkel Chazom and George Borba starring the team. In his second season as coach of the team they reached the AFC Champions League final, finishing second in the tournament. After two years as head coach of Hapoel Tel Aviv, Rosenbaum left his position and coached various teams, including Hapoel Kfar Saba, which won a game 4-0 against Hapoel Tel Aviv under his coaching, and then Hapoel Petah Tikva, from which he was fired in 1973 when the team was in danger of relegation, eight rounds from the end of the season. In 1976 he returned to Hapoel Tel Aviv and coached another season, which ended disappointingly as the team finished tenth. Afterward Rosenbaum managed the Hapoel Tel Aviv youth team for many years.
