Witzig is a product of the youth academies of Tägerwilen, Münchwilen, Wil and St. Gallen. He began his senior career with the reserves of St. Gallen in 2017. On 24 June 2021, he signed his first professional contract with St. Gallen, tying him to the club until June 2023. He made his professional debut with St. Gallen in a 3–1 Swiss [Super League] loss to Sion on 27 November 2021.