The 1962–63 William & Mary Indians men's basketball team represented the College of William & Mary in intercollegiate basketball during the 1962–63 NCAA University Division men's basketball season. Under the sixth year of head coach Bill Chambers, the team finished the season 15–9 and 10–5 in the Southern Conference. The Indians finished in 3rd place in the conference and qualified for the 1963 Southern Conference Men's Basketball Tournament, held at the Richmond Arena. Third-seeded William & Mary, however, fell to sixth-seeded VPI in the first round.