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Building upon recent progress in applying on-shell amplitude techniques to classical observables in general relativity, we propose a closed-form formula for the conservative Hamiltonian of a spinning binary system at the 1st post-Minkowskian (1PM) order. It is applicable for general compact spinning bodies with arbitrary spin multipole moments. The formula is linear in gravitational constant by definition, but exact to all orders in momentum and spin expansions. At each spin order, our formuladoi:10.1007/jhep05(2020)105 fatcat:u4h54p72jrejpk4devmaxn7xwm