On 3 July, Williams was selected to represent New Zealand in the men's rugby sevens at the 2016 Summer Olympics. His sister, Niall, was also selected to represent New Zealand in the women's tournament. On 9 August, in New Zealand's first game of the tournament, against Japan, Williams partially ruptured his Achilles tendon early in the second half. The injury ended Williams' Olympic campaign; New Zealand eventually finished in fifth place.