Toronto selected Horwitz out of Radford University in the 24th round of the 2019 draft. He was named an Appalachian League All-Star that year while playing for Bluefield. In 2021 at High-A Vancouver, he had a Northwest League-record 28-game hitting streak. He played for both Double-A New Hampshire and Triple-A Buffalo in 2022, and was promoted to the major-league Blue Jays on June 16, 2023. He made his MLB debut two days later as a designated hitter against the Texas Rangers and hit a single on the second pitch he faced.

Spencer played left field for Team Israel in the 2023 World Baseball Classic. He was named Eastern League Player of the Week on June 13, 2022 while playing for the New Hampshire Fisher Cats.