We present an effective field theory of the ∆-resonance as an interacting Weinberg's (3/2, 0) ⊕ (0, 3/2) field in the multi-spinor formalism. We derive its interactions with nucleons N , pions π and photons γ, and compute the ∆-resonance cross-sections in pion-nucleon scattering and pion photo-production. The theory contains only the physical spin-3/2 degrees of freedom. Thus, it is intrinsically consistent at the Hamiltonian level and, unlike the commonly used Rarita-Schwinger framework, does not require any additional ad hoc manipulation of couplings or propagators. The symmetries of hadronic physics select a unique operator for each coupling N π∆ and γπ∆. The proposed framework can be extended to also describe other higher-spin hadronic resonances.