In a sense you DO detect quarks experimentally.If you cannot detect quarks by themselves, what logic is used to experimentally detect an amount of spin or a magnetic moment to the quarks?
In deep inelastic scattering a single electron interacts via a single photon exchange with a single quark. This interactions itself can be described perturbatively and reveals some information regarding the nucleon structure in terms of quarks (and gluons). The structure of the nucleon is encoded in so-called structure functions fn(x,Q²) saying that a certain particle species n (up-, down, strange, ..., anti-up, ..., gluon, ...) carries a certain fraction x of the total nucleon momentum when probed at a certain energy Q (carried by the exchanged photon).
You can find the kinematics of DIS and the detailed definiton of the structure functions in http://arxiv.org/abs/0812.3535v2
In DIS the logic is that the nuceon structure is intrinsically non-perturbative and that the quarks and gluons are confined in a highly non-trivial manner, but that the interaction with the electron via the exchanged photon is well-described perturbatively. This last assumption is based on the so-called asymptotic freedom which says that a large momentum transfer quarks (and gluons) behave like free particles. This assumption can be cast in a mathematical expression and is proven to be valid as in the so-called scaling limit the above mentioned structure functions are Q-independent, i.e. F(x,Q²) → F(x). Small Q-dependence enters via so-called scaling violations still treated perturbatively. In this regime where the quarks behave like free particles their individual spin and magnetic moment is that of free spin 1/2 particles.
What we are discussing here is more complex than this simple explanation b/c we talk about so-called polarized or spin structure functions; the description can again be found in the article. The basic ideas regarding perturbative interaction of single electrons with asymptotic free quarks in the scaling limit is similar.