A bracket pin assembly includes a support plate having an end plate which has at least one opening. The pin includes a base, a support member, a first installation member, a second installation member, and a resilient member. The base has a chamber and the support member is connected to the base. The first and second installation members respectively have a first engaging portion and a second engaging portion. The support member has an engaging section. The resilient member is located in the chamber of the base to bias the first and second installation members. When the installation members of the pin extend through the first installation holes of the first post, the first and second engaging portions are engaged with the engaging section of the support members to secure the first and second installation members relative to the support members.