Born in Bernstadt (now called Bierutów), the capital of the Duchy of Bernstadt in Silesia, she was the fifth of the seven children of Duke Christian Ulrich I of Württemberg-Oels and his first wife, Anna Elisabeth, a daughter of Prince Christian II of Anhalt-Bernburg and Eleonore Sophie of Schleswig-Holstein-Sonderburg.
From her father's later marriages she had eight half-siblings, of whom only three survive adulthood: Charles Frederick II, Duke of Württemberg-Oels, Christian Ulrich II, Duke of Württemberg-Wilhelminenort (both sons of Sibylle Maria) and Auguste Louise (daughter of Sophie Wilhelmine; by marriage Duchess of Saxe-Weissenfels-Barby).
In Öls on 23 April 1699, Sophie Angelika married Prince Frederick Henry of Saxe-Zeitz.
Shortly after, he received from his older brother Maurice Wilhelm, Duke of Saxe-Zeitz, the towns of Pegau and Neustadt as appanage.
Sophie Angelika and her husband settled their residence in Pegau, where she died aged 23 after only nineteen months of childless union.