What is the spin of a quark?

Fermions are one of the two fundamental classes of particles, the other being bosons. Fermion particles are described by Fermi–Dirac statistics and have quantum numbers described by the Pauli exclusion principle. They include the quarks and leptons, as well as any composite particles consisting of an odd number of these, such as all baryons and many atoms and nuclei.

Fermions have half-integer spin; for all known elementary fermions this is 1⁄2. All known fermions except neutrinos, are also Dirac fermions; that is, each known fermion has its own distinct antiparticle. It is not known whether the neutrino is a Dirac fermion or a Majorana fermion.[4] Fermions are the basic building blocks of all matter. They are classified according to whether they interact via the strong interaction or not. In the Standard Model, there are 12 types of elementary fermions: six quarks and six leptons.

Quarks have spin 1/2 because they are fermions.