Sorotzkin was a son in law of the Telzer rav and rosh yeshiva, Rabbi Eliezer Gordon. When Gordon died in 1910, Sorotzkin was offered the position as rabbi and rosh yeshiva in Telz. He did not accept the position and was shortly after appointed as Rabbi to Voranava, Belarus (near Vilna). This enabled him to establish a close relationship with Rabbi Chaim Ozer Grodzenski. In Voranava, Rabbi Sorotzkin established a yeshiva ketana. After two years in Voranava, Rabbi Sorotzkin moved to Dziatłava (known as Zhetel or זשעטל in Yiddish), where he served as rabbi for eighteen years. As Zhetel was the birthplace of the Chofetz Chaim, the Chofetz Chaim would affectionately refer to Rabbi Sorotzkin as "my" rav.
In 1914, owing to the German invasion, Rabbi Sorotzkin moved to Minsk and became a close friend of the Chazon Ish, who rented a room from Rabbi Sorotzkin. Upon the end of the war, Rabbi Sorotzkin returned to Zhetel.
In 1930, he was appointed rabbi in Lutsk, where he remained until World War II. During the early days of the war, when many yeshivas had to relocate, Sorotzkin served as the head of the Vaad Hayeshivos, at the behest of Chaim Ozer Grodzenski. Sorotzkin managed to flee the war and escape to Mandate Palestine.
When the Moetzes Gedolei HaTorah (Council of Torah Sages) of the Agudath Israel was founded in Israel, Sorotzkin was appointed vice chairman. In 1953, the Chinuch Atzmai was formed and Sorotzkin was chosen to head it.
Sorotzkin authored the works, Oznaim LaTorah, a commentary on the Torah, Moznaim LaTorah, on the Jewish festivals, Sheailos Utshuvos Moznaim LaMishpat and HaDeah ve-ha-Dibur which is a collection of derashot.