Smart was admitted to Pembroke College on 20 October 1739 as a sizar under Leonard Addison. Although it is unclear why he chose Pembroke College, Addison was named in Peter Smart's trust deed (1729). As a sizar, he occasionally had to wait on the "Fellows' table" and perform other menial tasks. On 12 July 1740, he was awarded the "Dr. Watt's Foundation scholarship", which granted him six pounds a year until he gained a Bachelor of Arts degree. In addition to this income, he was also granted four pounds a year for scholarship. Although he was successful academically, he began to run up debt in order to pay for his extravagant lifestyle while at the college.