He attended the College of New Jersey where he graduated in 1761. He was licensed to preach in August of 1763. In October 1764 he was sent to the congregations of Greenwich, Oxford, and Mansfield Woodhouse, all in western New Jersey. In December 1764 he became a Presbyterian minister. By 1765, he was asked to serve neighboring congregations in Upper and Lower Hardwick in Warren County, New Jersey. In 1766, Rev. Rosbrugh married Jane Ralston. She was the daughter of James Ralston of East Allen Township, Northampton County, Pennsylvania. It was then called 'the Irish Settlement.' In 1769 Rev. Rosbrugh was called to serve at the church at Allen Township. This was the same congregation his wife was from. He became their permanent minister. For seven years, he led his congregation in Allen township.