In January 2015 he was named a Preseason First Team All-American by D3baseball.com. He was named 2015 All-SCIAC First Team, and named a 2015 "Jewish Sports Review" College Baseball All-American with, among others, first baseman/outfielder Jeremy Wolf and designated hitter/pitcher Jake Fishman. For his senior thesis, he evaluated the impact of the Major League Baseball collective bargaining agreement on the first-year player draft. For his college career he batted .376 with 23 home runs, 64 doubles, and over 160 RBIs, while pitching to a 7-3 record. In 2015 Rosenbaum played for the Vermont Mountaineers of the New England Collegiate Baseball League. He batted .245/.288/.327 with no home runs and six RBIs in 49 at bats. After college, Rosenbaum was a player/coach for the Brussels Kangaroos in Belgium. Rosenbaum plays for the Israel National Baseball Team. In the summer of 2014 Rosenbaum played for Israel at the 2014 European Pool C Championships qualifying round in Ljubljana, Slovenia, at which Israel won the tournament. He was named the Tournament MVP, as he was 9-for-17 with four home runs and 10 RBIs. Rosenbaum played for Team Israel in the B Pool in Vienna, Austria, in 2015. He played for Team Israel at the 2019 European Baseball Championship, and hit the game-tying home run in the 2019 B Pool Championship game against Russia in the bottom of the 8th. He also played for the team at the Africa/Europe 2020 Olympic Qualification tournament in Italy in September 2019, which Israel won to qualify to play baseball at the 2020 Summer Olympics in Tokyo. He played right field and DH and batted .133/.167/.133 in the tournament. In 2017 Rosenbaum was an advance scouting intern with the Tampa Bay Rays. In January 2019 he was hired by the Rays as a coordinator for baseball development.